Math Softwares
# gnuplot
## example
~~~
$ gnuplot
> set terminal qt
> set parametric
> set urange [a:b]
> set vrange [c:d]
> set title ""
> splot x(u,v), y(u,v), z(u,v)
~~~
2d-plot
~~~
> set parametric
> set terminal png
> set samples 1000000
> set output "sinlogcosexp.png"
> set trange [0:4.9]
> plot sin(log(t))*cos(exp(t)), sin(exp(t))*cos(log(t))
~~~
this is
# sage
# gap
## Gröbner basis
caclculate Gröbner basis $G$
~~~
gap>
gap> Q := Rationals;;
gap> x := Indeterminate(Q, "x");;
gap> y := Indeterminate(Q, "y");;
gap> ideal := [x^3 - 3*x^2 - y + 1, -x^2 + y^2 - 1];;
gap> lex := MonomialLexOrdering(x,y);;
gap> G := ReducedGroebnerBasis(ideal, lex);;
gap> Display(G);
[ y^5+y^4-11*y^3-17*y^2+9*y+17, -y^4+x*y+11*y^2-x+3*y-13, x^2-y^2+1 ]
~~~
$G$
- $ y^5 + y^4 - 11 y ^ 3 - 17 y ^ 2 + 9 y + 17 $
- $ - y ^ 4 + xy + 11 y ^ 2 - x+ 3y - 13 $
- $ x ^ 2 - y ^ 2 + 1 $
is Gröbner basis of
- $ x^3-3x^2-y+1 $
- $ -x^2+y^2-1 $