CoCalc Public Filesteaching / math-3012b / notes / multiplying_polynomials.sagewsOpen with one click!
Author: Fidel Barrera-Cruz
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Compute Environment: Ubuntu 18.04 (Deprecated)
p1=sum([x^(25*i) for i in range(4)]) p2=sum([x^(5*i) for i in range(16)]) show(p1) show(p2) show(expand(p1*p2))
x75+x50+x25+1\displaystyle x^{75} + x^{50} + x^{25} + 1
x75+x70+x65+x60+x55+x50+x45+x40+x35+x30+x25+x20+x15+x10+x5+1\displaystyle x^{75} + x^{70} + x^{65} + x^{60} + x^{55} + x^{50} + x^{45} + x^{40} + x^{35} + x^{30} + x^{25} + x^{20} + x^{15} + x^{10} + x^{5} + 1
x150+x145+x140+x135+x130+2x125+2x120+2x115+2x110+2x105+3x100+3x95+3x90+3x85+3x80+4x75+3x70+3x65+3x60+3x55+3x50+2x45+2x40+2x35+2x30+2x25+x20+x15+x10+x5+1\displaystyle x^{150} + x^{145} + x^{140} + x^{135} + x^{130} + 2 \, x^{125} + 2 \, x^{120} + 2 \, x^{115} + 2 \, x^{110} + 2 \, x^{105} + 3 \, x^{100} + 3 \, x^{95} + 3 \, x^{90} + 3 \, x^{85} + 3 \, x^{80} + 4 \, x^{75} + 3 \, x^{70} + 3 \, x^{65} + 3 \, x^{60} + 3 \, x^{55} + 3 \, x^{50} + 2 \, x^{45} + 2 \, x^{40} + 2 \, x^{35} + 2 \, x^{30} + 2 \, x^{25} + x^{20} + x^{15} + x^{10} + x^{5} + 1
cookies=sum([x^(2*i) for i in range(1,5)]) brownies=x^2+x^3+x^4+x^5 bread=sum([x^(i) for i in range(2,9)]) show(cookies) show(brownies) show(bread) show(expand(cookies*brownies*bread))
x8+x6+x4+x2\displaystyle x^{8} + x^{6} + x^{4} + x^{2}
x5+x4+x3+x2\displaystyle x^{5} + x^{4} + x^{3} + x^{2}
x8+x7+x6+x5+x4+x3+x2\displaystyle x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2}
x21+2x20+4x19+6x18+8x17+10x16+12x15+13x14+13x13+12x12+10x11+8x10+6x9+4x8+2x7+x6\displaystyle x^{21} + 2 \, x^{20} + 4 \, x^{19} + 6 \, x^{18} + 8 \, x^{17} + 10 \, x^{16} + 12 \, x^{15} + 13 \, x^{14} + 13 \, x^{13} + 12 \, x^{12} + 10 \, x^{11} + 8 \, x^{10} + 6 \, x^{9} + 4 \, x^{8} + 2 \, x^{7} + x^{6}