CRL 1.8 Functions MrG 2011.0920

3711 days ago by calcpage123

#1) var('y,a,z') f(x)=x^3-10*x^2+31*x-30 show(f(0)) show(f(y)) show(f(2)) show(f(a)) show(f(3)) show(f(5)) show(f(y*z)) show(f(1)) show(f(-3)) show(expand(f(x-2))) show(f(-1)) show(-6*f(6)) 
       
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\newcommand{\Bold}[1]{\mathbf{#1}}y^{3} z^{3} - 10 \, y^{2} z^{2} + 31 \, y z - 30
\newcommand{\Bold}[1]{\mathbf{#1}}-8
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\newcommand{\Bold}[1]{\mathbf{#1}}x^{3} - 16 \, x^{2} + 83 \, x - 140
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#3) phi(x)=x^4-55*x^2-210*x-216 show(f(2)) show(phi(-2)) show(f(3)) show(phi(-3)) show(f(5)) show(phi(-4)) show(f(0)+phi(0)+246) 
       
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#5) F(x)=x*(x-1)*(x+6)*(x-1/2)*(x+5/4) show(F(0)) show(F(1)) show(F(-6)) bool(F(1/2)==F(-5/4)) 
       
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#5a) def F(x): return x*(x-1)*(x+6)*(x-1/2)*(x+5/4) F(1/2)==F(-5/4) 
       
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#7) var('a,y,z') phi(x)=a^x (phi(y)*phi(z)).simplify() 
       
\newcommand{\Bold}[1]{\mathbf{#1}}a^{y + z}
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bool(phi(y)*phi(z)==phi(y+z)) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}{\rm True}
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#9) f(x)=cos(x) show(bool(f(x)==f(-x))) show(bool(f(x)==-f(pi-x))) show(bool(f(x)==-f(pi+x))) 
       
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#11) var('n,m') psi(x)=x^(2*n)+x^(2*m)+1 show(psi(1)) show(psi(0).simplify()) show(psi(a).simplify()) show(psi(-a).simplify()) 
       
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