jaxmate-pure v1.0.0 (type @help ;-)


> using lib::ptri;
> simplify $ df ((x+5)^3) x;
3*x^2+30*x+75
> redpp ans;

$\def\({\left(} \def\){\right)}\def\atan{\operatorname{atan}}\def\erf{\operatorname{erf}}\def\co{,}\def\[{}\def\]{}$ $$3\cdot x^{2}+30\cdot x+75$$ 
> let r = simplify $ intg (exp (2*x)) x;
> r;
e^(2*x)/2
> redpp r;

$\def\({\left(} \def\){\right)}\def\atan{\operatorname{atan}}\def\erf{\operatorname{erf}}\def\co{,}\def\[{}\def\]{}$ $$\frac{e^{2\cdot x}}{2}$$ 
> simplify $ solve (x^2+7) x;
[x==sqrt 7*i,x==-sqrt 7*i]
> redpp ans;

$\def\({\left(} \def\){\right)}\def\atan{\operatorname{atan}}\def\erf{\operatorname{erf}}\def\co{,}\def\[{}\def\]{}$ $$\{x=\[\sqrt{7}\cdot i\]\co x=\[-\sqrt{7}\cdot i\]\}$$ 
> redpp $  df (log(sin x)^2) x;

$\def\({\left(} \def\){\right)}\def\atan{\operatorname{atan}}\def\erf{\operatorname{erf}}\def\co{,}\def\[{}\def\]{}$ $$\frac{2\cdot \cos \(x\)\cdot \ln \(\sin \(x\)\)}{\sin \(x\)}$$ 
> declare depend [z,cos x,y];
()
> simplify (df (sin z) (cos x));
cos z*df z (cos x)
> redpp ans;

$\def\({\left(} \def\){\right)}\def\atan{\operatorname{atan}}\def\erf{\operatorname{erf}}\def\co{,}\def\[{}\def\]{}$ $$\cos \(z\)\cdot \frac{\partial z}{\partial \cos \(x\)}$$ 
> redpp (df (z^2) x);

$\def\({\left(} \def\){\right)}\def\atan{\operatorname{atan}}\def\erf{\operatorname{erf}}\def\co{,}\def\[{}\def\]{}$ $$2\cdot \frac{\partial z}{\partial x}\cdot z$$ 
> I a b n = simplify $ intg (x^2*(a*x+b)^n) x;
> I a b n;
((a*x+b)^n*a^3*n^2*x^3+3*(a*x+b)^n*a^3*n*x^3+2*(a*x+b)^n*a^3*x^3+(a*x+b)^n*a^2*b*n^2*x^2+(a*x+b)^n*a^2*b*n*x^2-2*(a*x+b)^n*a*b^2*n*x+2*(a*x+b)^n*b^3)/(a^3*n^3+6*a^3*n^2+11*a^3*n+6*a^3)
> redpp ans;

$\def\({\left(} \def\){\right)}\def\atan{\operatorname{atan}}\def\erf{\operatorname{erf}}\def\co{,}\def\[{}\def\]{}$ $$\frac{\(a\cdot x+b\)^{n}\cdot a^{3}\cdot n^{2}\cdot x^{3}+3\cdot \(a\cdot x+b\)^{n}\cdot a^{3}\cdot n\cdot x^{3}+2\cdot \(a\cdot x+b\)^{n}\cdot a^{3}\cdot x^{3}+\(a\cdot x+b\)^{n}\cdot a^{2}\cdot b\cdot n^{2}\cdot x^{2}+\(a\cdot x+b\)^{n}\cdot a^{2}\cdot b\cdot n\cdot x^{2}-2\cdot \(a\cdot x+b\)^{n}\cdot a\cdot b^{2}\cdot n\cdot x+2\cdot \(a\cdot x+b\)^{n}\cdot b^{3}}{a^{3}\cdot n^{3}+6\cdot a^{3}\cdot n^{2}+11\cdot a^{3}\cdot n+6\cdot a^{3}}$$ 
> simplify $ 'map (y=>df y x)   [x^n,x^m,sin x];
[x^n*n/x,x^m*m/x,cos x]
> redpp ans;

$\def\({\left(} \def\){\right)}\def\atan{\operatorname{atan}}\def\erf{\operatorname{erf}}\def\co{,}\def\[{}\def\]{}$ $$\{\frac{x^{n}\cdot n}{x}\co \frac{x^{m}\cdot m}{x}\co \cos \(x\)\}$$ 
> let f = 2/((x+1)^2*(x+2));
>  simplify $ pf f x;
[2/(x+2),(-2)/(x+1),2/(x^2+2*x+1)]
> redpp ans;

$\def\({\left(} \def\){\right)}\def\atan{\operatorname{atan}}\def\erf{\operatorname{erf}}\def\co{,}\def\[{}\def\]{}$ $$\{\frac{2}{x+2}\co \frac{-2}{x+1}\co \frac{2}{x^{2}+2\cdot x+1}\}$$ 
> reduce::switch "exp" 0 ;
0
>  redpp $ pf f x;

$\def\({\left(} \def\){\right)}\def\atan{\operatorname{atan}}\def\erf{\operatorname{erf}}\def\co{,}\def\[{}\def\]{}$ $$\{\frac{2}{x+2}\co \frac{-2}{x+1}\co \frac{2}{\(x+1\)^{2}}\}$$ 
> let eqn1 = log(sin (x+3))^5 == 8 ;
> let sol1 = simplify $ solve eqn1 x;
> sol1!0;
x==pi-3-asin (e^2^(3/5))+2*arbint 1*pi
> redpp ans;

$\def\({\left(} \def\){\right)}\def\atan{\operatorname{atan}}\def\erf{\operatorname{erf}}\def\co{,}\def\[{}\def\]{}$ $$x=\[\pi -3-\asin \(e^{2^{\frac{3}{5}}}\)+2\cdot arbint\(1\)\cdot \pi \]$$ 
> let s0 = {1,0;0,1} ; 
... let s1 = {0,1;1,0} ; 
... let s2 = {0,-i;i,0}; 
... let s3 = {1,0;0,-1};
> redpp s0;

$\def\({\left(} \def\){\right)}\def\atan{\operatorname{atan}}\def\erf{\operatorname{erf}}\def\co{,}\def\[{}\def\]{}$ $$\pmatrix{1&0\cr 0&1\cr }$$ 
> redpp [s0,s1,s2,s3];

$\def\({\left(} \def\){\right)}\def\atan{\operatorname{atan}}\def\erf{\operatorname{erf}}\def\co{,}\def\[{}\def\]{}$ $$\{\pmatrix{1&0\cr 0&1\cr }\co \pmatrix{0&1\cr 1&0\cr }\co \pmatrix{0&-i\cr i&0\cr }\co \pmatrix{1&0\cr 0&-1\cr }\}$$ 
> map (simplify.tp) [s1,s2,s3] ;
[{0,1;1,0},{0,i;-i,0},{1,0;0,-1}]
> redpp ans;

$\def\({\left(} \def\){\right)}\def\atan{\operatorname{atan}}\def\erf{\operatorname{erf}}\def\co{,}\def\[{}\def\]{}$ $$\{\pmatrix{0&1\cr 1&0\cr }\co \pmatrix{0&i\cr -i&0\cr }\co \pmatrix{1&0\cr 0&-1\cr }\}$$ 
> redpp  (1/{a11,a12;a21,a22}*{y1;y2}) ;

$\def\({\left(} \def\){\right)}\def\atan{\operatorname{atan}}\def\erf{\operatorname{erf}}\def\co{,}\def\[{}\def\]{}$ $$\pmatrix{\frac{-\(a_{12}\cdot y_{2}-a_{22}\cdot y_{1}\)}{a_{11}\cdot a_{22}-a_{12}\cdot a_{21}}\cr \frac{a_{11}\cdot y_{2}-a_{21}\cdot y_{1}}{a_{11}\cdot a_{22}-a_{12}\cdot a_{21}}\cr }$$ 
> simplify $ limit (1/x) x 0 ;
inf
> redpp ans;

$\def\({\left(} \def\){\right)}\def\atan{\operatorname{atan}}\def\erf{\operatorname{erf}}\def\co{,}\def\[{}\def\]{}$ $$\infty$$ 
> simplify $ odesolve [(df y x 2) == y] [y] x [[x==0,y==A],[x==1,y==B]] ;

*** depend y , x
[y==((A*e-B)*e-e^(2*x)*(A-B*e))/(e^x*(e^2-1))]
> declare depend [y,x]; 
()
> simplify $ odesolve [(df y x 2) == y] [y] x [[x==0,y==A],[x==1,y==B]] ;
[y==((A*e-B)*e-e^(2*x)*(A-B*e))/(e^x*(e^2-1))]
> redpp ans;

$\def\({\left(} \def\){\right)}\def\atan{\operatorname{atan}}\def\erf{\operatorname{erf}}\def\co{,}\def\[{}\def\]{}$ $$\{y=\[\frac{\(A\cdot e-B\)\cdot e-e^{2\cdot x}\cdot \(A-B\cdot e\)}{e^{x}\cdot \(e^{2}-1\)}\]\}$$ 
> simplify $ plot (sin x/x) (x=='(-15..15));
[]
>