{ "cells": [ { "cell_type": "markdown", "metadata": { "collapsed": false, "deletable": false, "editable": false }, "source": [ "# Lab 2: Lists, Loops and Animation\n", "\n", "One of the great things about computers is their ability to repeat tasks\n", "quickly, accurately and without getting bored. We will take advantage of this\n", "capability many times during this course. This lab will introduce loops, which\n", "perform such repetition, and use them to create animations. First, however,\n", "we’ll take a look at some of the different kinds of objects SageMath works with.\n", "\n", "### Types of Things\n", "\n", "In the previous lab, you worked with numbers and functions. You also made\n", "plots, and in the process of making them, you encountered words enclosed in\n", "quotation marks. For example, when you want to make a plot red, you have to\n", "put the word \"red\" in quotation marks. Such words are called strings, which is\n", "short for \"character strings\". Strings allow computers to handle words, phrases,\n", "and typographic symbols.\n", "Strings can include numbers, not just letters. But when numbers are treated\n", "as strings, they act quite differently from regular numbers.\n", "\n", "
\n", "Exercise 1. Enter the following code into SageMath and compare the outputs.\n", " \n", "```\n", ">>a=5\n", ">>show(a)\n", ">>b=\"5\"\n", ">>show(b)\n", "```\n", "Exercise 2. What happens when you add 1 to `a`? To `b`?\n", "
\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "5" ] }, "execution_count": 10, "metadata": { }, "output_type": "execute_result" }, { "data": { "text/html": [ "" ], "text/plain": [ "'5'" ] }, "execution_count": 10, "metadata": { }, "output_type": "execute_result" } ], "source": [ "a=5\n", "show(a)\n", "b=\"5\"\n", "show(b)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "6" ] }, "execution_count": 11, "metadata": { }, "output_type": "execute_result" } ], "source": [ "a+1" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "ename": "TypeError", "evalue": "unsupported operand parent(s) for +: '' and 'Integer Ring'", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mb\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m/ext/sage/sage-9.1/local/lib/python3.7/site-packages/sage/rings/integer.pyx\u001b[0m in \u001b[0;36msage.rings.integer.Integer.__add__ (build/cythonized/sage/rings/integer.c:12304)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1801\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1802\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1803\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mcoercion_model\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbin_op\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mleft\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mright\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moperator\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 1804\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1805\u001b[0m \u001b[0mcpdef\u001b[0m \u001b[0m_add_\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mright\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;32m/ext/sage/sage-9.1/local/lib/python3.7/site-packages/sage/structure/coerce.pyx\u001b[0m in \u001b[0;36msage.structure.coerce.CoercionModel.bin_op (build/cythonized/sage/structure/coerce.c:11178)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1253\u001b[0m \u001b[0;31m# We should really include the underlying error.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1254\u001b[0m \u001b[0;31m# This causes so much headache.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1255\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mbin_op_exception\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mop\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 1256\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1257\u001b[0m \u001b[0mcpdef\u001b[0m \u001b[0mcanonical_coercion\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mTypeError\u001b[0m: unsupported operand parent(s) for +: '' and 'Integer Ring'" ] } ], "source": [ "b+1" ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "#there was an error for the b funciton" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "deletable": false, "editable": false }, "source": [ "Remark. There is a little bit of vocabulary you should be aware of, as you may\n", "see it online and in the SageMath documentation. While the fundamental idea\n", "to understand is that different types of objects behave differently even though\n", "they may look alike, programmers often use the word \"type\" for simple objects\n", "like strings and numbers and \"class\" for more complex ones like graphs. Just\n", "think \"type\" when you see “class” and you’ll be fine.\n", "You can find out what the type of an object is using the type command.\n", "```\n", ">>type(a)\n", "\n", "```\n", "This output means that `a` is a SageMath integer.\n", "```\n", ">>type(b)\n", "\n", "```\n", "This output means that `b` is a character string.\n", "\n", "\n", "\n", "
\n", " Exercise 3. Find the types of the number 0.2 and the graph (plot) of $f(x) = x^2$. (Hint: Look back at the end of Lab 1 fo how to make a plot).\n", "
\n" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": { }, "output_type": "execute_result" } ], "source": [ "type (0.2)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 17, "metadata": { }, "output_type": "execute_result" } ], "source": [ "type(plot(x^2))" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "deletable": false, "editable": false }, "source": [ "In the above exercises, the variables a and b look the same when displayed\n", "using show but act very differently when used in an arithmetical calculation.\n", "This happens because a is the integer 5 while b is the character string \"5\". We\n", "say these variables have different types, which just means they’re different kinds\n", "of things. The type of a is \"integer\", while the type of b is \"string\".\n", "This explains what you saw in Exercise 2. Adding 1 to an integer is not a\n", "problem, but adding 1 to a character string makes no sense and results in an\n", "error.
\n", "Actually, addition is defined for strings in SageMath. Here’s how it works.\n", "\n", "```\n", ">>\"5\"+\"1\"\n", "'51'\n", "```\n", "\n", "You can see that the + symbol (or \"operator\") still embodies the idea of\n", "\"putting things together\". However, \"putting things together\" means something\n", "different for integers than for character strings or for the plots in Lab 1 #33, so the exact meaning of + changes depending on the types of objects it’s acting on. (Programmers say this makes + an overloaded operator.)\n", "\n", "
\n", " Exercise 4. Give another example of a type of SageMath object for which\n", "addition is defined and explain what addition means for that type of data.\n", "
" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "'53'" ] }, "execution_count": 18, "metadata": { }, "output_type": "execute_result" } ], "source": [ "\"5\"+\"3\"\n", "#this function is putting the two numbers together instead of adding them" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "deletable": false, "editable": false }, "source": [ "### Lists\n", "\n", "Scientific data and the outputs of model simulations often come in the form of\n", "lists of numbers. SageMath gives us many tools for working with such lists and\n", "tables.\n", "\n", "You make a list by enclosing its elements, separated by commas, in square\n", "brackets:\n", "```\n", "[\"Bacteria\", \"Protists\", \"Plants\", \"Fungi\", \"Animals\"]\n", "[2,3,5,7,11,13]\n", "```\n", "Each element of a list can be accessed by its position in the list, typically\n", "called its index. In Python, indexing starts with 0, so the first element of a list\n", "with $k$ elements has index 0 and the last element has index $k − 1$." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "deletable": false, "editable": false }, "source": [ "**Example 1.** Enter the list of biological kingdoms into SageMath and call it\n", "kingdoms.\n", "```\n", ">>kingdoms = [\"Bacteria\", \"Protists\", \"Plants\", \"Fungi\", \"Animals\"]\n", "```\n", "To access the first element of this list, enter:\n", "```\n", ">>kingdoms[0]\n", "'Bacteria'\n", "```\n", "
\n", "Exercise 5. A bacteria population is doubling every hour. Its sizes at different\n", "times are 100, 200, 400 and 800. Make a list of these values.\n", " \n", "[100, 200, 400, 800]\n", " \n", "Exercise 6. Assign the list of bacteria population sizes to the variable\n", "`bacteria`. (You can just copy and paste the list.)\n", " \n", "Exercise 7. Find the type of the variable `bacteria` from the previous exercise.\n", " \n", "Exercise 8. What is the value of `bacteria[1]`? What about `bacteria[0]`?\n", "First, answer without entering the command into SageMath. Then, use SageMath to check your answers.\n", "
" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[100, 200, 400, 800]" ] }, "execution_count": 5, "metadata": { }, "output_type": "execute_result" } ], "source": [ "[100,200,400,800]" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "bacteria=[100,200,400,800]" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": { }, "output_type": "execute_result" } ], "source": [ "type(bacteria)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "100" ] }, "execution_count": 7, "metadata": { }, "output_type": "execute_result" } ], "source": [ "bacteria[1]\n", "bacteria[0]" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "deletable": false, "editable": false }, "source": [ "You can add an element to the end of a list using listname.append(element).\n", "(The generic names listname or list are just placeholders for the real name of\n", "your list.) For instance if you wanted to add the string “Archaea” to the list\n", "named kingdoms, the code would look something like this:\n", "```\n", ">> kingdoms.append(\"Archaea\")\n", "```\n", "Note that the above code does not output anything to the screen. This\n", "is because the `append()` function only tells the computer to save its input to\n", "specified list. To see the result, we would have to type `kingdoms` and evaluate\n", "the cell.\n", "\n", "
\n", " Exercise 9. Append the number 1600 to `bacteria` and call it to display its\n", "value. Don’t paste or retype any output.
\n", "[100, 200, 400, 800, 1600]\n", " \n", "Exercise 10. What is the next value of the population? Append it to the list.\n", " \n", "Exercise 11. What would happen in the example above if we did\n", "kingdoms.append(\"Archaea\") twice before viewing kingdoms? Try this out\n", "and explain why you got the result that you did.\n", "
" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[100, 200, 400, 800, 1600, 3200, 1600, 1600]" ] }, "execution_count": 16, "metadata": { }, "output_type": "execute_result" } ], "source": [ "bacteria.append(1600)\n", "bacteria" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[100, 200, 400, 800, 1600, 3200, 1600, 1600, 3200, 3200]" ] }, "execution_count": 18, "metadata": { }, "output_type": "execute_result" } ], "source": [ "bacteria.append(3200)\n", "bacteria" ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "#displaying kingdom.append(archea) twice, would add archea to the list twice. This because now multiple strings of archea have been inputed" ] }, { "attachments": { "lab2_ll_f1.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": { "collapsed": false, "deletable": false, "editable": false }, "source": [ "### Plotting lists\n", "\n", "To plot the entries in a list, use the `list_plot` function. If you give this function\n", "a single list of numbers as an input, it will plot each number against its position\n", "in the list. For example, the command `list_plot(bacteria)` plots the list of population\n", "sizes you just created in Example 6, producing the graph below.\n", "\n", "\n", "\n", "Notice that the $x$-coordinate of the first point is 0, not 1. This happens\n", "because SageMath starts counting at zero, so the index of the first element of a\n", "list is 0.\n", "\n", "
\n", "Exercise 12. Plot the list [3,5,7,9,11].\n", "
" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 25, "metadata": { }, "output_type": "execute_result" } ], "source": [ "odds=[3,5,7,9,11]\n", "list_plot(odds)" ] }, { "attachments": { "lab2_ll_f2a.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": { "collapsed": false, "deletable": false, "editable": false }, "source": [ "Often, we will need to plot lists of points. For example, suppose we have the\n", "points (1,2), (2,1), (3,4), and (4,3), with the first number in the ordered pair\n", "an $x$-coordinate and the second a $y$-coordinate. How do we plot these points in\n", "SageMath?\n", "\n", "First, we enter the list of points:\n", "```\n", ">>g = [(1,2), (2,1), (3,4), (4,3)]\n", "```\n", "Then, we use the list_plot function to produce the figure below\n", "```\n", ">>list_plot(g)\n", "```\n", "\n", "\n", "This plot is technically correct, but the points are a little hard to see. To\n", "make them more noticeable, we might color them red and change their size.\n", "The command `list_plot(g, color=\"red\", size=30)` produces the second figure below.\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "deletable": false, "editable": false }, "source": [ "
\n", "Exercise 13. Define your own list of pairs of values and plot it. Make sure\n", "your plot is legible.\n", "
" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "evens=[(2,2), (4,4),(6,6),(8,8)]" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", 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" 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" } }, "cell_type": "markdown", "metadata": { "collapsed": false, "deletable": true, "editable": true }, "source": [ "Whether you’re plotting a list of numbers using `list_plot()` or a mathematical\n", "function using `plot()`, you can label the axes of the plot using the\n", "`axes_labels` plotting option.\n", "\n", "
\n", " Example 2. Adding axes labels to our plot of bacteria population sizes.\n", " \n", "```\n", "list_plot(bacteria, axes_labels=[\"time\", \"population\"])\n", "```\n", "\n", "
\n", " \n", "Notice that axes_labels is a variable that we set equal to a list of labels.\n", "In SageMath, square brackets always mean that a list is involved.\n", "Another feature of list_plot is the ability to connect the points of the list\n", "together. This is accomplished by using the plotjoined option:\n", "
\n", "Example 3. Making the bacteria graph plot joined and adding axes labels:\n", " \n", "```\n", "list_plot(bacteria, axes_labels=[\"time\",\"population\"],plotjoined = True)\n", "```\n", "\n", "
\n", "\n", "Note that the value of `plotjoined` is either `True` or `False`. This type of data\n", "is called a boolean. You will learn more about this data type in the future.\n", "Now that we know how to label axes and join points, we should do so whenever\n", "it is reasonable to do so. We should join points whenever we want to see a\n", "curve. Labeling axes is a good way to keep track of which values correspond to\n", "which axes, especially when we plot lists against each other." ] }, { "attachments": { "lab2_ll_f4.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": { "collapsed": false, "deletable": false, "editable": false }, "source": [ "However, `list_plot` requires a list of points, not two lists of numbers, as\n", "input. To avoid typing long lists of points and all the required parentheses by\n", "hand, we turn to the function `zip`. This function takes two lists and turns them\n", "into a list of ordered pairs. (It can also take more than two lists and turn them\n", "into a list of $n$-tuples.) Actually, for reasons that are beyond the scope of this\n", "class, we have to next apply the `list` function to the output of `zip`. For example:\n", "```\n", ">>list(zip([1,2,3], [4,5,6]))\n", "[(1, 4), (2, 5), (3, 6)]\n", ">>list(zip([1,2,3], [4,5,6], [7,8,9]))\n", "[(1, 4, 7), (2, 5, 8), (3, 6, 9)]\n", "```\n", "This is the kind of input that `list_plot` needs. It’s common to nest the `list(zip())`\n", "command inside the list_plot command, as below.\n", "```\n", ">>list_plot(list(zip([1,2,3], [4,5,6])))\n", "```\n", "This means the same thing as:\n", "```\n", ">>pairs = list(zip([1,2,3], [4,5,6]))\n", ">>list_plot(pairs)\n", "```\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "deletable": true, "editable": true }, "source": [ "
\n", " Exercise 14. You are studying populations of hippos and crocodiles in a river\n", "in Africa. Over five years, the hippo population at your study site has been 62,\n", "81, 75, 90 and 67. In the same years, the crocodile population has been 20, 34,\n", "18, 25 and 31. Plot the system’s states in hippo-crocodile space, labeling your\n", "axes appropriately and making the points red.\n", "
" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 12, "metadata": { }, "output_type": "execute_result" } ], "source": [ "hippo_crocodile=list(zip([62,81,75,90,67], [20,34,18,25,31]))\n", "list_plot(hippo_crocodile, axes_labels=[\"hippos\",\"crocodiles\"],color=\"red\")" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "deletable": false, "editable": false }, "source": [ "The `zip` function is very helpful in plotting time series graphs. All you\n", "need to do is make a list of time values and `zip` it with the values of your state\n", "variable. It is usually used together with the `list` function which converts the output of `zip` into a list. \n", "
\n", "Exercise 15. The list in Exercise 10 gives the size of a population of bacteria\n", "at one-hour intervals. Since one hour is 1/24 of a day, create a list of time points\n", "for these observations with time in days. Then, plot a time series graph of the\n", "population.\n", "
" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 13, "metadata": { }, "output_type": "execute_result" } ], "source": [ "bacteria\n", "time=[1.0/24,2.0/24,3.0/24,4.0/24,5.0/24,6.0/24]\n", "btime=list(zip(time,bacteria))\n", "list_plot(btime, axes_labels=[\"time\",\"bacteria\"])" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "deletable": false, "editable": false }, "source": [ "Having developed some basic tools, we will now use them to work with\n", "real data. Your worksheet contains lists called `wt5_time`, `wt5_heartrate` and\n", "`wt5_temp`. These lists contain heart rate and body temperature data for a wild\n", "type (control) rat, measured over 72 hours as part of a real study of circadian\n", "rhythms.\n", "
\n", "Exercise 16. Plot time series of the rat’s heart rate and body temperature,\n", "using different colors. Make sure the plot uses the given time values, not just 0,\n", "1, 2.... and that your axes are labeled.\n", " \n", "Exercise 17. Compare the plots and describe any relationships you observe.\n", " \n", "Exercise 18. Plot the data as a trajectory in temperature-heart rate space.\n", "Make sure to label your axes.\n", "
" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "verbose 0 (163: primitive.py, options) WARNING: Ignoring option 'axes_lables'=['time', 'heart rate']\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "verbose 0 (163: primitive.py, options) \n", "The allowed options for Point set defined by 289 point(s) are:\n", " alpha How transparent the point is. \n", " faceted If True color the edge of the point. (only for 2D plots) \n", " hue The color given as a hue. \n", " legend_color The color of the legend text \n", " legend_label The label for this item in the legend. \n", " marker the marker symbol for 2D plots only (see documentation of plot() for details)\n", " markeredgecolorthe color of the marker edge (only for 2D plots) \n", " rgbcolor The color as an RGB tuple. \n", " size How big the point is (i.e., area in points^2=(1/72 inch)^2).\n", " zorder The layer level in which to draw \n", "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "verbose 0 (163: primitive.py, options) WARNING: Ignoring option 'axes_lables'=['time', 'heart rate']\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "verbose 0 (163: primitive.py, options) \n", "The allowed options for Point set defined by 289 point(s) are:\n", " alpha How transparent the point is. \n", " faceted If True color the edge of the point. (only for 2D plots) \n", " hue The color given as a hue. \n", " legend_color The color of the legend text \n", " legend_label The label for this item in the legend. \n", " marker the marker symbol for 2D plots only (see documentation of plot() for details)\n", " markeredgecolorthe color of the marker edge (only for 2D plots) \n", " rgbcolor The color as an RGB tuple. \n", " size How big the point is (i.e., area in points^2=(1/72 inch)^2).\n", " zorder The layer level in which to draw \n", "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "verbose 0 (163: primitive.py, options) WARNING: Ignoring option 'axes_lables'=['time', 'heart rate']\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "verbose 0 (163: primitive.py, options) \n", "The allowed options for Point set defined by 289 point(s) are:\n", " alpha How transparent the point is. \n", " faceted If True color the edge of the point. (only for 2D plots) \n", " hue The color given as a hue. \n", " legend_color The color of the legend text \n", " legend_label The label for this item in the legend. \n", " marker the marker symbol for 2D plots only (see documentation of plot() for details)\n", " markeredgecolorthe color of the marker edge (only for 2D plots) \n", " rgbcolor The color as an RGB tuple. \n", " size How big the point is (i.e., area in points^2=(1/72 inch)^2).\n", " zorder The layer level in which to draw \n", "\n" ] }, { "data": { "image/png": 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", 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[0,0.25,0.5,0.75,1,1.25,1.5,1.75,2,2.25,2.5,2.75,3,3.25,3.5,3.75,4,4.25,4.5,4.75,5,5.25,5.5,5.75,6,6.25,6.5,6.75,7,7.25,7.5,7.75,8,8.25,8.5,8.75,9,9.25,9.5,9.75,10,10.25,10.5,10.75,11,11.25,11.5,11.75,12,12.25,12.5,12.75,13,13.25,13.5,13.75,14,14.25,14.5,14.75,15,15.25,15.5,15.75,16,16.25,16.5,16.75,17,17.25,17.5,17.75,18,18.25,18.5,18.75,19,19.25,19.5,19.75,20,20.25,20.5,20.75,21,21.25,21.5,21.75,22,22.25,22.5,22.75,23,23.25,23.5,23.75,24,24.25,24.5,24.75,25,25.25,25.5,25.75,26,26.25,26.5,26.75,27,27.25,27.5,27.75,28,28.25,28.5,28.75,29,29.25,29.5,29.75,30,30.25,30.5,30.75,31,31.25,31.5,31.75,32,32.25,32.5,32.75,33,33.25,33.5,33.75,34,34.25,34.5,34.75,35,35.25,35.5,35.75,36,36.25,36.5,36.75,37,37.25,37.5,37.75,38,38.25,38.5,38.75,39,39.25,39.5,39.75,40,40.25,40.5,40.75,41,41.25,41.5,41.75,42,42.25,42.5,42.75,43,43.25,43.5,43.75,44,44.25,44.5,44.75,45,45.25,45.5,45.75,46,46.25,46.5,46.75,47,47.25,47.5,47.75,48,48.25,48.5,48.75,49,49.25,49.5,49.75,50,50.25,50.5,50.75,51,51.25,51.5,51.75,52,52.25,52.5,52.75,53,53.25,53.5,53.75,54,54.25,54.5,54.75,55,55.25,55.5,55.75,56,56.25,56.5,56.75,57,57.25,57.5,57.75,58,58.25,58.5,58.75,59,59.25,59.5,59.75,60,60.25,60.5,60.75,61,61.25,61.5,61.75,62,62.25,62.5,62.75,63,63.25,63.5,63.75,64,64.25,64.5,64.75,65,65.25,65.5,65.75,66,66.25,66.5,66.75,67,67.25,67.5,67.75,68,68.25,68.5,68.75,69,69.25,69.5,69.75,70,70.25,70.5,70.75,71,71.25,71.5,71.75,72]\n", "wt5_temp = [35.77,37.23,37.32,36.75,36.09,35.68,35.46,35.35,35.3,35.21,35.21,35.25,35.4,35.92,36.52,36.56,36.07,35.6,35.39,35.27,35.09,34.91,34.85,34.81,34.78,34.85,34.88,34.96,35.05,34.96,34.8,34.76,34.73,34.74,35.18,35.91,36.31,36.39,36.12,35.59,35.27,35.17,35,34.69,34.53,34.85,35.49,35.98,35.89,35.34,35,35.37,36.25,36.62,36.51,36.77,37.32,37.76,37.95,38.01,38.03,38.05,38.02,37.95,37.93,37.88,37.69,37.53,37.51,37.56,37.61,37.6,37.6,37.65,37.61,37.51,37.14,36.4,35.72,35.44,35.36,35.27,35.32,35.65,36.2,36.61,36.96,37.33,37.62,37.8,37.86,37.84,37.82,37.81,37.75,37.68,37.63,37.52,37.3,36.82,36.13,35.68,35.52,35.57,35.66,35.62,35.42,35.28,35.64,36.13,36.01,35.61,35.37,35.29,35.2,35.15,35.18,35.18,35.07,35.02,35.05,35,35.02,35.1,35.02,35.08,35.49,35.89,35.78,35.38,35.11,34.96,34.97,35.09,35.07,34.85,34.69,34.99,35.45,35.38,35.02,34.81,34.83,35.34,36.18,36.83,37.14,37.06,36.5,35.94,36.06,36.65,37.23,37.66,37.86,37.84,37.73,37.68,37.67,37.63,37.48,37.3,37.45,37.7,37.78,37.8,37.78,37.71,37.68,37.75,37.75,37.69,37.6,37.48,36.91,36.01,35.3,35.09,35.12,35.21,35.41,35.84,36.59,37.13,37.42,37.64,37.71,37.77,37.91,37.96,37.92,37.87,37.76,37.59,37.27,36.75,36.08,35.53,35.23,35.05,34.95,35.06,35.26,35.35,35.39,35.26,35.13,35.37,36.06,36.48,36.11,35.6,35.31,35.09,34.94,34.96,34.97,34.89,34.88,34.96,35.07,34.99,34.77,34.62,34.67,34.85,35.08,35.5,35.63,35.25,34.9,34.8,34.81,34.85,34.87,34.84,34.92,35.35,36.03,36.64,37.08,37.23,36.85,36.07,35.64,35.75,35.89,36.23,36.96,37.56,37.87,37.97,37.98,37.93,37.81,37.65,37.58,37.62,37.49,36.99,36.27,35.89,36.29,37.03,37.51,37.71,37.77,37.76,37.74,37.79,37.85,37.8,37.78,37.68,37.45,37.31,37.2,36.81,36.15,35.69,35.62,35.64,35.5,35.35,35.4,35.93,36.72,37.25,37.47]\n", "wt5_heartrate = [331.47,410.62,463.32,480.56,473.31,459.9,452.98,454.75,461.56,470.87,484.46,505.84,534.55,562.83,578.89,574.82,552.25,520.8,491.4,470.81,460.3,457.16,456.96,456.11,453.75,451.48,451.06,452.29,453.44,453.55,454.49,461.06,478.03,505.51,536.27,558.56,563.27,549.66,525.12,499.9,481.87,475.01,480.79,498.93,525.28,549.9,560.69,552.6,533.76,520.3,523.28,540.41,560.34,573.63,578.49,578.02,574.9,570.02,564.09,558.59,554.81,552.92,552.29,552.27,552.39,552.24,551.57,550.63,550.19,550.88,552.73,555.04,556.38,554.57,547.06,532.59,512.76,491.6,473.03,459.32,452.36,455.58,472.62,503.18,540.53,574.07,595.23,601.76,597.62,589.4,582.49,579.13,578.75,579.31,578.58,574.91,567.41,556.08,541.99,527.21,514.02,503.74,496.21,490.82,488.54,492.6,505.66,525.36,543.11,549.4,541.17,523.96,506.83,495.72,491.37,491.71,494.49,497.69,498.8,495.44,487.4,478.19,473.99,480.22,497.57,520.13,537.52,540.95,529.09,508.91,490.2,479.05,476.1,479.64,488.66,501.97,515.35,521.91,517.48,506.06,498.71,505.08,525.26,549.53,565.84,568.35,560.79,553.23,554.81,567.03,582.81,592.37,590.95,581.33,569.71,560.1,552.83,546.82,542.14,540.11,541.58,545.37,548.68,549.15,546.78,543.85,543.01,545.34,549.85,554.01,554.52,548.03,532.35,508.52,481.79,459.69,448.17,449.67,464.37,491.41,526.74,561.1,583.36,587.92,578.53,564.48,553.59,548.63,548.51,551.01,554.27,556.99,557.78,554.81,546.51,532.93,516.34,499.85,485.46,473.6,464.31,458.29,456.62,460.16,469.8,486.63,509.82,533.63,548.04,545.19,526.28,501.47,481.99,472.29,469.38,467.99,465.25,461.21,457.09,454.15,453.41,455.56,461.25,471.6,487.59,507.33,524.65,532.4,528.34,516.93,504.55,494.12,485.64,481.11,486.37,506.26,538.25,571.75,593.88,596.72,580.97,555.18,532.03,522.91,532.44,556.03,582.79,602.15,609.44,606.79,599.74,593.11,588.75,585.99,583.12,578.26,569.53,556.26,541.45,532.31,535.95,552.76,574.56,590.46,594.96,590.47,583.31,578.29,576.74,577.61,579.03,579.39,577.66,573.25,565.19,551.64,530.99,504.17,475.89,452.9,440.63,441.7,457.24,487.39,528.77,572.1,605.2,619.96,616.62]\n", "heart=list(zip(wt5_time,wt5_heartrate))\n", "temp=list(zip(wt5_time,wt5_temp))\n", "list_plot(heart,color=\"red\",axes_lables=[\"time\",\"heart rate\"])" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 21, "metadata": { }, "output_type": "execute_result" } ], "source": [ "list_plot(temp,color=\"blue\",axes_labels=[\"time\",\"temperature\"])" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "#both of the graphs oscillate, but the minimum and maximum values are diferent." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 25, "metadata": { }, "output_type": "execute_result" } ], "source": [ "tempheart=list(zip(wt5_temp,wt5_heartrate))\n", "list_plot(tempheart,plotjoined=true, axes_labels=[\"temperature\",\"heart rate\"])" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "deletable": false, "editable": false }, "source": [ "### For loops\n", "\n", "Suppose you wanted to print out a series of sentences listing your favorite foods.\n", "You might use the print command and write:\n", "```\n", "print(\"Pizza is one of my favorite foods.\")\n", "print(\"Chocolate is one of my favorite foods.\")\n", "print(\"Green curry is one of my favorite foods.\")\n", "```\n", "This works, but it’s rather tedious, especially if you like many kinds of food.\n", "A shortcut would be useful.\n", "\n", "Looking at the example, you can see that the `print` command and the string\n", "\" is one of my favorite foods.\" are the same in every line. The only thing that\n", "changes is the name of the food. It would be convenient if we could just make\n", "a list of the foods and insert them into the code one at a time.\n", "\n", "We can do this using something called a *for loop*. One way to handle the\n", "foods example with a for loop is the following:\n", "```\n", "favorites = [\"Pizza\", \"Chocolate\", \"Green curry\"]\n", "for food in favorites:\n", " print(food + \" is one of my favorite foods.\")\n", "```\n", "In this example, `food` is a variable that takes on the value \"Pizza\" the\n", "first time the computer executes the statement print food + \" is one of\n", "my favorite foods.\", \"Chocolate\" the second time and \"Green curry\" the\n", "third time.\n", "\n", "
\n", "Exercise 19. Print out sentences listing five of your favorite books, songs or\n", "movies using a for loop.\n", "
" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Up is one of my favorite movies\n", "Shrek is one of my favorite movies\n", "Meet the Robinsons is one of my favorite movies\n" ] } ], "source": [ "favorites=[\"Up\",\"Shrek\",\"Meet the Robinsons\"]\n", "for movies in favorites:\n", " print(movies + \" is one of my favorite movies\")" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "deletable": true, "editable": true }, "source": [ "More generally, a for loop in SageMath (or Python) has the form:\n", "```\n", "for var in list:\n", " loop body\n", "```\n", "The loop body must be indented. After the loop body, go back to your\n", "previous level of indentation.\n", "\n", "\n", "**Example 4.** A string is similar in most ways to a list. This loop will print\n", "each character in the word “dynamics” on a separate line.\n", "```\n", ">>for char in \"dynamics\":\n", ">> print(char)\n", "d\n", "y\n", "n\n", "a\n", "m\n", "i\n", "c\n", "s\n", "```\n", "\n", "\n", "As you can see, the variable given immediately after the word for takes on\n", "the value of each list element in turn. First char was \"d\", then it was \"y\", then\n", "\"n\", and so on. This is the key to how SageMath for loops work. The body\n", "of the loop is executed for each element in the list. The body stays the same,\n", "while the list element changes. When writing loops, think about what should\n", "stay the same and what should change.\n", "\n", "**Example 5.** The following loop computes the base-10 logarithm of 10, 100,\n", "and 1000 in SageMath:\n", "```\n", ">>for val in [10, 100, 1000]:\n", ">> print(log(val, 10))\n", "1\n", "2\n", "3\n", "```\n", "\n", "\n", "
\n", "Exercise 20.Use a for loop to print your name vertically.\n", " \n", "Exercise 21. Use a for loop to square the numbers 15, 27, 39 and 84.\n", " \n", "```\n", "225\n", "729\n", "1521\n", "7056\n", "```\n", "\n" ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "collapsed": false, "deletable": false, "editable": false }, "outputs": [ ], "source": [ ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "M\n", "a\n", "k\n", "a\n", "y\n", "l\n", "a\n" ] } ], "source": [ "for char in \"Makayla\":\n", " print(char)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "225\n", "729\n", "1521\n", "7056\n" ] } ], "source": [ "for val in [15,27,39,84]:\n", " print(val^2)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "deletable": false, "editable": false }, "source": [ "## Things to Do with Lists and Loops\n", "\n", "### Using loops to make lists\n", "\n", "In the previous exercises, you used loops to output values. Often, it is useful to\n", "store these values in a list.\n", "\n", "To start, you’ll need to create a list with no elements. (Think of this as\n", "tearing out a piece of paper and titling it “Groceries” when making a shopping\n", "list.) To make such an empty list, enter `listname = []`. Then, use\n", "`listname.append()` to add computed values to your list.\n", "\n", "**Example 6.** This code makes a list of the first ten multiples of 2.\n", "```\n", ">>mult2 = [] #Set up empty list\n", ">>for n in [1,2,3,4,5,6,7,8,9,10]:\n", ">> mult2.append(2*n) #Compute the n’th multiple of 2 and append to list\n", ">>mult2 #Display the list\n", "[2, 4, 6, 8, 10, 12, 14, 16, 18, 20]\n", "```\n", "
\n", "Exercise 22. Make a list containing the first five multiples of 3.
\n", "[3, 6, 9, 12, 15]\n", " \n", "Exercise 23. Write a loop that makes a list of the squares of the numbers 0.1,\n", "0.2, $\\dots$, 0.7. Then, plot your list.\n", " \n", "[0.0100000000000000, 0.0400000000000000, 0.0900000000000000,\n", "0.160000000000000, 0.250000000000000, 0.360000000000000,\n", "0.490000000000000]\n", " \n", "Exercise 24. Create a function and apply it to the numbers 0 through 5,\n", "inclusive. Plot the list of resulting values.\n", "
" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[3, 6, 9, 12, 15]" ] }, "execution_count": 32, "metadata": { }, "output_type": "execute_result" } ], "source": [ "mult3=[]\n", "for n in [1,2,3,4,5]:\n", " mult3.append(3*n)\n", "mult3" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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aGhrS1taWnp6eEeM9PT1ZtGjRSc+799578+u//uu555578s53vvPn3qexsTFTp04dsQEAlKGqd5aSZM2aNVmxYkXa29vT0dGR7u7u9PX1ZeXKlUmOdYX27t2bLVu2JDkWlG677bZ85jOfyfXXXz/clTr//PPT1NQ0ih8FAGD0VR2Wli9fnoMHD2bDhg3p7+/PvHnzsm3btsyaNStJ0t/fP2LOpc997nN59dVXs2rVqqxatWp4/Pbbb89f/dVfnfknAAAYQ1XPs1QG8ywBAGWxNhwAQAFhCQCggLAEAFBAWAIAKCAsAQAUEJYAAAoISwAABWo6LG3cuDFz5szJggULyi4FADhHmZQSAKBATXeWAADKJiwBABQQlgAACghLAAAFhCUAgALCEgBAAWEJAKCAsAQAUEBYAsaVgweTf/mX5Ac/KLsS4FwhLAHjxje+kbzpTcmiRckVVyTPPVd2RcC5QFgCxo0/+7OfdpQOHEg+8Yly6wHODTUdliykC/z/GhtH7k+eXE4dwLnFQrrAuPH97yc33ZR897vHvo776leTlpayqwImukllFwBwqt7whuTb305efDGZPj2pry+7IuBcICwB48qkScmMGWVXAZxLavqdJQCAsglLAAAFhCUAgALCEgBAAWEJAKCAsAQAUEBYAgAoICwBABQQlgAACtR0WLKQLgBQNgvpAgAUqOnOEgBA2YQlAIACwhIAQAFhCQCggLAEAFBAWAIAKCAsAQAUEJYAAAoISwAABYQlAIACwhIAQIGaDksW0gUAymYhXQCAAjXdWQIAKJuwBABQQFgCACggLAEAFBCWAAAKCEsAAAWEJQCAAqcVljZt2pTW1tZMnjw5bW1t2bFjx0mP7e/vz6233porrrgi5513XlavXn3axQIAnG1Vh6WtW7dm9erVWbduXXbt2pXFixdn6dKl6evrO+Hxg4ODueSSS7Ju3bpcc801Z1wwAMDZVPUM3gsXLsz8+fOzefPm4bHZs2dn2bJl6erqKjz3rW99a6699trcfffdVRVpBm8AoCxVdZaOHDmS3t7edHZ2jhjv7OzMzp07R62owcHBDAwMjNgAAMpQVVg6cOBAhoaG0tzcPGK8ubk5+/btG7Wiurq60tTUNLy1tLSM2rUBAKpxWi9419XVjdivVCrHjZ2JtWvX5tChQ8Pbnj17Ru3aAADVmFTNwdOmTUt9ff1xXaT9+/cf1206E42NjWlsbBy16wEAnK6qOksNDQ1pa2tLT0/PiPGenp4sWrRoVAsDAKgFVXWWkmTNmjVZsWJF2tvb09HRke7u7vT19WXlypVJjn2Ftnfv3mzZsmX4nN27dydJXnnllbz44ovZvXt3GhoaMmfOnFH6GFBbvvWt5Iknkrlzkze/uexqADgTVYel5cuX5+DBg9mwYUP6+/szb968bNu2LbNmzUpybBLKn51z6brrrhv+ube3N/fcc09mzZqV73//+2dWPdSg3t5k8eLk//7v2P5f/mXyG79Rbk0AnL6q51kqg3mWGE/+4A+ST37yp/uLFydPPllePQCcGWvDwSh7/euL9wEYX6r+Gg4otmpV8o1vJA8/fOydpSonrAegxvgaDgCggK/hAAAKCEsAAAWEJQCAAjUdljZu3Jg5c+ZkwYIFZZcCAJyjvOANAFCgpjtLAABlE5YAAAoISwAABYQlAIACwhIAQAFhCQCggLAEAFBAWAIAKCAsAQAUEJYAAAoISwAABWo6LFlIFwAom4V0AQAK1HRnCQCgbMISAEABYQkAoICwBABQQFgCACggLAEAFBCWAAAKCEsAAAWEJQCAAsLSOeyBB5J3vSu5885kYKDsagCgNk0quwDKsXNn8p73JEePHtv/7/9O7r+/3JoAoBbVdGfJQrpj5+mnfxqUkuTrXy+vFgCoZRbSPUc980xy/fXJ0NCx/VtvTf72b8utCQBqka/hzlHt7cm2bck99yQzZyZr15ZdEQDUJp0lAIACNf3OEgBA2YQlAIACwhIAQAFhCQCggLAEAFBAWAIAKCAsAQAUEJYAAAoISwAABYQlAIACNR2WNm7cmDlz5mTBggVllwIAnKOsDQcAUKCmO0sAAGUbF2HpRz8quwIA4FxV82HpjjuSGTOO/fxP/1RuLQDAuaem31navj1561uTZCBJU6ZOPZRDh7yzBACcPTXdWXrllZH7P/pRcvRoObUAAOemmg5LN92U3HDDT/c//OHkvJquGACYaM5a9Ni0aVNaW1szefLktLW1ZceOHT/3nMbG5LHHfvqu0h/+4RgXCQDwM85KWNq6dWtWr16ddevWZdeuXVm8eHGWLl2avr6+n3tuQ0OyePFZKBIA4ATOygveCxcuzPz587N58+bhsdmzZ2fZsmXp6ur6ueeblBIAKMuYd5aOHDmS3t7edHZ2jhjv7OzMzp07x/r2AABnZNJY3+DAgQMZGhpKc3PziPHm5ubs27fvhOcMDg5mcHBweH9gYGBMawQAOJmz9oJ3XV3diP1KpXLc2E90dXWlqalpeGtpacldd92VCy+88GyUCgAwbMw7S9OmTUt9ff1xXaT9+/cf1236ibVr12bNmjUjxhobG08argAAxsqYd5YaGhrS1taWnp6eEeM9PT1ZtGjRCc9pbGzM1KlTR2yNjY1jXSoAwHHGvLOUJGvWrMmKFSvS3t6ejo6OdHd3p6+vLytXrjwbtwcAOG1nJSwtX748Bw8ezIYNG9Lf35958+Zl27ZtmTVr1tm4PQDAaavphXQBAMpmpTUAgALCEgBAAWEJAKCAsAQAUEBYAgAoICwBABQ4K/MsnUilUsnLL79c1u0BgHPUhRdeWNUSaqWFpZdffjlNTU1l3R4AOEcdOnQoU6dOPeXjS5uUsprO0sDAQFpaWrJnz56qPtzPWrBgQZ5++unTPn80r1Mr16ilZzvRfn8827G5xmg919GoZbSuUSu1TMRnWyu/P57t2F3ndJ7tuOks1dXVVf0H5ieL6p6u+vr6M/5DOlrXqZVr/EQtPNuJ9vvzE57t2NRyps91tGrxbMeullq5xmhex7Mdu+uMxrM9mXPqBe9Vq1bVzHVq5RqjpZY+Ty3VMhpq6fPUUi2joZY+Ty3VMhpq5fPU0u/PaKmV5zIRn+3JjIu14QYGBtLU1FT1d4z8fJ7t2PFsx4bnOnY827Hj2Y6ds/Fs69evX79+TK48yurr6/PWt741kyaV9s3hhOXZjh3Pdmx4rmPHsx07nu3YGetnOy46SwAAZTmn3lkCAKiWsAQAUEBYAgAoICwBABSo+bC0adOmtLa2ZvLkyWlra8uOHTvKLmlCePLJJ3PzzTfn0ksvTV1dXR588MGyS5oQurq6smDBglx44YWZPn16li1blu985ztllzUhbN68OVdfffXwxHMdHR15+OGHyy5rQurq6kpdXV1Wr15ddinj3vr161NXVzdi+8Vf/MWyy5ow9u7dm1/7tV/LxRdfnAsuuCDXXnttent7R/0+NR2Wtm7dmtWrV2fdunXZtWtXFi9enKVLl6avr6/s0sa9w4cP55prrslnP/vZskuZULZv355Vq1blX//1X9PT05NXX301nZ2dOXz4cNmljXuXXXZZPv7xj+eZZ57JM888k7e97W255ZZb8txzz5Vd2oTy9NNPp7u7O1dffXXZpUwYc+fOTX9///D27LPPll3ShPDDH/4wN9xwQ17zmtfk4Ycfzje/+c186lOfyute97pRv1dNTx2wcOHCzJ8/P5s3bx4emz17dpYtW5aurq4SK5tY6urq8uUvfznLli0ru5QJ58UXX8z06dOzffv2vPnNby67nAnnoosuyic+8Ym8//3vL7uUCeGVV17J/Pnzs2nTpnz0ox/Ntddem7vvvrvsssa19evX58EHH8zu3bvLLmXCueuuu/K1r33trHzjVLOdpSNHjqS3tzednZ0jxjs7O7Nz586SqoLqHDp0KMmx/6gzeoaGhnLffffl8OHD6ejoKLucCWPVqlV55zvfmZtuuqnsUiaU559/PpdeemlaW1vzvve9Ly+88ELZJU0IDz30UNrb2/Oe97wn06dPz3XXXZfPf/7zY3Kvmg1LBw4cyNDQUJqbm0eMNzc3Z9++fSVVBaeuUqlkzZo1+eVf/uXMmzev7HImhGeffTavfe1r09jYmJUrV+bLX/5y5syZU3ZZE8J9992Xf/u3f9O1H2ULFy7Mli1b8sgjj+Tzn/989u3bl0WLFuXgwYNllzbuvfDCC9m8eXMuv/zyPPLII1m5cmV+93d/N1u2bBn1e9X8nOt1dXUj9iuVynFjUIvuuOOO/Pu//3ueeuqpskuZMK644ors3r07L730Uu6///7cfvvt2b59u8B0hvbs2ZM777wzjz76aCZPnlx2ORPK0qVLh3++6qqr0tHRkTe+8Y3567/+66xZs6bEysa/o0ePpr29PR/72MeSJNddd12ee+65bN68Obfddtuo3qtmO0vTpk1LfX39cV2k/fv3H9dtglrzwQ9+MA899FAef/zxXHbZZWWXM2E0NDTkl37pl9Le3p6urq5cc801+cxnPlN2WeNeb29v9u/fn7a2tkyaNCmTJk3K9u3b8+d//ueZNGlShoaGyi5xwpgyZUquuuqqPP/882WXMu7NmDHjuP9Rmj179pj8JbCaDUsNDQ1pa2tLT0/PiPGenp4sWrSopKqgWKVSyR133JEHHnggjz32WFpbW8suaUKrVCoZHBwsu4xxb8mSJXn22Weze/fu4a29vT2/+qu/mt27d6e+vr7sEieMwcHBfOtb38qMGTPKLmXcu+GGG46bmuU//uM/MmvWrFG/V01/DbdmzZqsWLEi7e3t6ejoSHd3d/r6+rJy5cqySxv3Xnnllfznf/7n8P73vve97N69OxdddFFmzpxZYmXj26pVq3LPPffkH/7hH3LhhRcOd0abmppy/vnnl1zd+PZHf/RHWbp0aVpaWvLyyy/nvvvuyxNPPJGvfOUrZZc27l144YXHvVc3ZcqUXHzxxd63O0Mf+tCHcvPNN2fmzJnZv39/PvrRj2ZgYCC333572aWNe7/3e7+XRYsW5WMf+1je+9735utf/3q6u7vT3d09+jer1LiNGzdWZs2aVWloaKjMnz+/sn379rJLmhAef/zxSpLjtttvv73s0sa1Ez3TJJUvfOELZZc27v3mb/7m8L8LLrnkksqSJUsqjz76aNllTVhvectbKnfeeWfZZYx7y5cvr8yYMaPymte8pnLppZdW3v3ud1eee+65ssuaMP7xH/+xMm/evEpjY2PlyiuvrHR3d4/JfWp6niUAgLLV7DtLAAC1QFgCACggLAEAFBCWAAAKCEsAAAWEJQCAAsISAEABYQkAoICwBABQQFgCACggLAEAFBCWAAAK/D+t8oXccW/NcAAAAABJRU5ErkJggg==", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 33, "metadata": { }, "output_type": "execute_result" } ], "source": [ "square=[]\n", "for n in [0.1,0.2,0.3,0.4,0.5,0.6,0.7]:\n", " square.append(n^2)\n", "square\n", "list_plot(square)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[6, 8, 10, 12, 14, 16]" ] }, "execution_count": 34, "metadata": { }, "output_type": "execute_result" } ], "source": [ "func=[]\n", "for n in [0,1,2,3,4,5]:\n", " func.append(2*n+6)\n", "func" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "deletable": false, "editable": false }, "source": [ "We can use loops to process data.\n", "
\n", "Exercise 25. The time in wt5_time is measured in hours. Create another list\n", "in which it is given in minutes.\n", " \n", "Exercise 26. Convert the temperatures in wt5_temp from Celsius to Fahrenheit.\n", "(The formula is $F = (9/5) C + 32$.)\n", " \n", "\n", "Exercise 27. Plot a time series of your transformed data.\n", " \n", "Exercise 28. Plot a trajectory of the transformed temperature data and the\n", "original heart rate data.\n", "
\n" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "minutes=[]\n", "for x in wt5_temp:\n", " minutes.append(x/60.0)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "cel = []\n", "for x in wt5_temp:\n", " cel.append((9/5)*x+32)" ] }, { "cell_type": "raw", "metadata": { "collapsed": false }, "source": [ "timeseries=list(zip(minutes,cel))\n", "list_plot(timeseries)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 40, "metadata": { }, "output_type": "execute_result" } ], "source": [ "trajectory=list(zip(cel,wt5_heartrate))\n", "list_plot(trajectory, plotjoined=true)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false, "deletable": false, "editable": false }, "source": [ "## Animations\n", "\n", "When investigating functions and models, it can be useful to animate their\n", "response to changes in parameters. Sage’s animate function allows us to easily\n", "produce such animations.\n", "\n", "Animations are created by showing a series of still images one after the other,\n", "fast enough to create the illusion of motion. The animate function takes a list\n", "of plots as input and animates it.\n", "\n", "**Example 7.** The following code shows how a change in the slope of a line\n", "affects the line’s appearance.\n", "```\n", "plots = [] #Set up empty list to hold plots\n", "slopes = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5] #Make a list of slopes\n", "for m in slopes: #For each m in slope, create plot, add to list\n", " p=plot(m*x, (x,-10,10))\n", " plots.append(p)\n", "a=animate(plots) #Create the animation\n", "show(a) #Necessary to display the animation\n", "```\n", "Try this code now. The show command is necessary to view the animation;\n", "it can also be used with other graphics.\n", "\n", "Oops! The code produces an animation all right, but the animation is useless\n", "because it’s the axes, not the line, that move. To stop this from happening, we\n", "can specify maximum and minimum values for $y$, fixing the $y$-axis in place.\n", "\n", "**Example 8.** Fixing the y-axis in an animation\n", "```\n", "plots = [] #Set up empty list to hold plots\n", "slopes = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5] #Make a list of slopes\n", "for m in slopes: #For each m in slope, create plot, add to list\n", " p=plot(m*x, (x,-10,10), ymin=-50, ymax=50)\n", " plots.append(p)\n", "a=animate(plots) #Create the animation\n", "show(a) #Necessary to display the animation\n", "```\n", "This code produces a useful animated plot.\n", "
\n", "Exercise 29. Change the animation in Example 8 to make the line green rather\n", "than blue.\n", "\n", "Exercise 30. Change the previous animation to make the slope range from -3\n", "to 3 in steps of 0.5.\n", " \n", "Exercise 31. Rewrite the animation in Exercise 29 so that the slope of the line\n", "plotted is always 1 but the $y$-intercept ranges between -5 and 5.\n", "
" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": false }, "outputs": [ { "ename": "TypeError", "evalue": "'list' object is not callable", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0mslopes\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m 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\u001b[0mymin\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m50\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mymax\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m50\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mcolor\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"green\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 5\u001b[0m \u001b[0mplots\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0manimate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mplots\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mTypeError\u001b[0m: 'list' object is not callable" ] } ], "source": [ "plots = []\n", "slopes = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5]\n", "for m in slopes:\n", " p=plot(m*x, (x,-10,10), ymin=-50, ymax=50,color=\"green\")\n", " plots.append(p)\n", "a=animate(plots)\n", "show(a)" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false }, "outputs": [ { "ename": "TypeError", "evalue": "'list' object is not callable", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0mslopes\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mRealNumber\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'2.5'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mRealNumber\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'1.5'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mRealNumber\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'0.5'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mRealNumber\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'0.5'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mRealNumber\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'1.5'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mRealNumber\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'2.5'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mm\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mslopes\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0mp\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mm\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mymin\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m50\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mymax\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m50\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcolor\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"green\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 5\u001b[0m \u001b[0mplots\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0manimate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mplots\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mTypeError\u001b[0m: 'list' object is not callable" ] } ], "source": [ "plots = []\n", "slopes = [-3,-2.5,-2,-1.5,-1,-0.5,0,0.5,1,1.5,2,2.5,3]\n", "for m in slopes:\n", " p=plot(m*x, (x,-3,3), ymin=-50, ymax=50, color=\"green\")\n", " plots.append(p)\n", "a=animate(plots)\n", "show(a)" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": false }, "outputs": [ { "ename": "TypeError", "evalue": "'list' object is not callable", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0myint\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mm\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mslopes\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0mp\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mymin\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m50\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mymax\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m50\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 5\u001b[0m \u001b[0mplots\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0manimate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mplots\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mTypeError\u001b[0m: 'list' object is not callable" ] } ], "source": [ "plots = []\n", "yint = [-5,-4,-3,-2,-1,0,1,2,3,4,5]\n", "for m in slopes:\n", " p=plot(1*x+b, (x,-10,10), ymin=-50, ymax=50)\n", " plots.append(p)\n", "a=animate(plots)\n", "show(a)" ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.1", "language": "sagemath", "metadata": { "cocalc": { "description": "Open-source mathematical software system", "priority": 10, "url": "https://www.sagemath.org/" } }, "name": "sage-9.1" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 4 }