CoCalc Public Fileshyperspherical.ipynb
Author: Cristina Sanz Sanz
Views : 85
Description: Could you please help me to understand what the problem is with the solving of the system of equations? Thank you in advance. Cristina
In [20]:
var('r2 si co')
assume(r12>0,r22>0,r32>0,d32>0)
eq1 = r12==r2*d32*(1.-si*(co+(3.0*(1-co*co))^(1./2.))/2.)/2.
eq2 = r22==r2*d32*(1.-si*(co-(3.0*(1-co*co))^(1./2.))/2.)/2.
eq3 = r32==r2*d32*(1.+si*co)/2.0
eq1.show()
eq2.show()
eq3.show()

$r_{12} = 0.500000000000000 \, {\left(-0.500000000000000 \, {\left(\mathit{co} + \sqrt{-3.00000000000000 \, \mathit{co}^{2} + 3.00000000000000}\right)} \mathit{si} + 1.00000000000000\right)} d_{32} r_{2}$
$r_{22} = 0.500000000000000 \, {\left(-0.500000000000000 \, {\left(\mathit{co} - \sqrt{-3.00000000000000 \, \mathit{co}^{2} + 3.00000000000000}\right)} \mathit{si} + 1.00000000000000\right)} d_{32} r_{2}$
$r_{32} = 0.500000000000000 \, {\left(\mathit{co} \mathit{si} + 1.00000000000000\right)} d_{32} r_{2}$
In [21]:
solve([eq1,eq2,eq3],r2,si,co)

--------------------------------------------------------------------------- TypeError Traceback (most recent call last) <ipython-input-21-23b2cb9ba4cb> in <module>() ----> 1 solve([eq1,eq2,eq3],r2,si,co) /ext/sage/sage-8.1/local/lib/python2.7/site-packages/sage/symbolic/relation.pyc in solve(f, *args, **kwds) 1048 s = [] 1049 -> 1050 sol_list = string_to_list_of_solutions(repr(s)) 1051 1052 # Relaxed form suggested by Mike Hansen (#8553): /ext/sage/sage-8.1/local/lib/python2.7/site-packages/sage/symbolic/relation.pyc in string_to_list_of_solutions(s) 578 from sage.structure.sequence import Sequence 579 from sage.calculus.calculus import symbolic_expression_from_maxima_string --> 580 v = symbolic_expression_from_maxima_string(s, equals_sub=True) 581 return Sequence(v, universe=Objects(), cr_str=True) 582 /ext/sage/sage-8.1/local/lib/python2.7/site-packages/sage/calculus/calculus.pyc in symbolic_expression_from_maxima_string(x, equals_sub, maxima) 2157 _augmented_syms = {} 2158 except SyntaxError: -> 2159 raise TypeError("unable to make sense of Maxima expression '%s' in Sage"%s) 2160 finally: 2161 is_simplified = False TypeError: unable to make sense of Maxima expression '[if((-pi/2<parg(-((3*_SAGE_VAR_r22-3*_SAGE_VAR_r12)*sqrt(_SAGE_VAR_r32^2+((-_SAGE_VAR_r22)-_SAGE_VAR_r12)*_SAGE_VAR_r32+_SAGE_VAR_r22^2-_SAGE_VAR_r12*_SAGE_VAR_r22+_SAGE_VAR_r12^2))/(2*_SAGE_VAR_r32^2+((-2*_SAGE_VAR_r22)-2*_SAGE_VAR_r12)*_SAGE_VAR_r32+2*_SAGE_VAR_r22^2-2*_SAGE_VAR_r12*_SAGE_VAR_r22+2*_SAGE_VAR_r12^2)))and(parg(-((3*_SAGE_VAR_r22-3*_SAGE_VAR_r12)*sqrt(_SAGE_VAR_r32^2+((-_SAGE_VAR_r22)-_SAGE_VAR_r12)*_SAGE_VAR_r32+_SAGE_VAR_r22^2-_SAGE_VAR_r12*_SAGE_VAR_r22+_SAGE_VAR_r12^2))/(2*_SAGE_VAR_r32^2+((-2*_SAGE_VAR_r22)-2*_SAGE_VAR_r12)*_SAGE_VAR_r32+2*_SAGE_VAR_r22^2-2*_SAGE_VAR_r12*_SAGE_VAR_r22+2*_SAGE_VAR_r12^2))<==pi/2),[_SAGE_VAR_co==-((2*_SAGE_VAR_r32-_SAGE_VAR_r22-_SAGE_VAR_r12)*sqrt(_SAGE_VAR_r32^2+((-_SAGE_VAR_r22)-_SAGE_VAR_r12)*_SAGE_VAR_r32+_SAGE_VAR_r22^2-_SAGE_VAR_r12*_SAGE_VAR_r22+_SAGE_VAR_r12^2))/(2*_SAGE_VAR_r32^2+((-2*_SAGE_VAR_r22)-2*_SAGE_VAR_r12)*_SAGE_VAR_r32+2*_SAGE_VAR_r22^2-2*_SAGE_VAR_r12*_SAGE_VAR_r22+2*_SAGE_VAR_r12^2),_SAGE_VAR_r2==(2*_SAGE_VAR_r32+2*_SAGE_VAR_r22+2*_SAGE_VAR_r12)/(3*_SAGE_VAR_d32),_SAGE_VAR_si==-(2*sqrt(_SAGE_VAR_r32^2+((-_SAGE_VAR_r22)-_SAGE_VAR_r12)*_SAGE_VAR_r32+_SAGE_VAR_r22^2-_SAGE_VAR_r12*_SAGE_VAR_r22+_SAGE_VAR_r12^2))/(_SAGE_VAR_r32+_SAGE_VAR_r22+_SAGE_VAR_r12)],union()),if((-pi/2<parg(((3*_SAGE_VAR_r22-3*_SAGE_VAR_r12)*sqrt(_SAGE_VAR_r32^2+((-_SAGE_VAR_r22)-_SAGE_VAR_r12)*_SAGE_VAR_r32+_SAGE_VAR_r22^2-_SAGE_VAR_r12*_SAGE_VAR_r22+_SAGE_VAR_r12^2))/(2*_SAGE_VAR_r32^2+((-2*_SAGE_VAR_r22)-2*_SAGE_VAR_r12)*_SAGE_VAR_r32+2*_SAGE_VAR_r22^2-2*_SAGE_VAR_r12*_SAGE_VAR_r22+2*_SAGE_VAR_r12^2)))and(parg(((3*_SAGE_VAR_r22-3*_SAGE_VAR_r12)*sqrt(_SAGE_VAR_r32^2+((-_SAGE_VAR_r22)-_SAGE_VAR_r12)*_SAGE_VAR_r32+_SAGE_VAR_r22^2-_SAGE_VAR_r12*_SAGE_VAR_r22+_SAGE_VAR_r12^2))/(2*_SAGE_VAR_r32^2+((-2*_SAGE_VAR_r22)-2*_SAGE_VAR_r12)*_SAGE_VAR_r32+2*_SAGE_VAR_r22^2-2*_SAGE_VAR_r12*_SAGE_VAR_r22+2*_SAGE_VAR_r12^2))<==pi/2),[_SAGE_VAR_co==((2*_SAGE_VAR_r32-_SAGE_VAR_r22-_SAGE_VAR_r12)*sqrt(_SAGE_VAR_r32^2+((-_SAGE_VAR_r22)-_SAGE_VAR_r12)*_SAGE_VAR_r32+_SAGE_VAR_r22^2-_SAGE_VAR_r12*_SAGE_VAR_r22+_SAGE_VAR_r12^2))/(2*_SAGE_VAR_r32^2+((-2*_SAGE_VAR_r22)-2*_SAGE_VAR_r12)*_SAGE_VAR_r32+2*_SAGE_VAR_r22^2-2*_SAGE_VAR_r12*_SAGE_VAR_r22+2*_SAGE_VAR_r12^2),_SAGE_VAR_r2==(2*_SAGE_VAR_r32+2*_SAGE_VAR_r22+2*_SAGE_VAR_r12)/(3*_SAGE_VAR_d32),_SAGE_VAR_si==(2*sqrt(_SAGE_VAR_r32^2+((-_SAGE_VAR_r22)-_SAGE_VAR_r12)*_SAGE_VAR_r32+_SAGE_VAR_r22^2-_SAGE_VAR_r12*_SAGE_VAR_r22+_SAGE_VAR_r12^2))/(_SAGE_VAR_r32+_SAGE_VAR_r22+_SAGE_VAR_r12)],union())]' in Sage 
In [8]:
var('a')
solve(x^2-a,x)

[x == -sqrt(a), x == sqrt(a)]
In [ ]: