x = polygen (QQ, 'x')
p1=-3*x+7*x^2 -3*x^3+7*x ^4; p2=5*x^5+3*x^3+x^2 -2*x+1;p1 ; p2
7x4
− 3x3
+ 7x2
− 3x
5x5
+ 3x3
+ x2
− 2x + 1
p1*p2 ;
35x9
− 15x8
+ 56x7
− 17x6
+ 4x5
+ 11x4
− 20x3
+ 13x2
− 3x
(q , r ) = p2 . quo_rem( p1 ) ; q ; r
5
7
x +
15
49
−
53
49
x3
+ x2
−
53
49
x + 1
f a c t o r ( p1 ) ; maxima . gfactor ( p1 )
(7) · (x −
3
7
) · x · (x2
+ 1)
x (x − i) (x + i) (7 x − 3)
var ( 'y') ; x , y=polygens (QQ, 'x , y')
y
pol=6*x*y^5+12*y^4+14*y^3*x^3 -15*x^2*y^3+9*x^3*y^2 -35*x^4*y+21*x ^5; pol
14x3
y3
+ 6xy5
+ 21x5
− 35x4
y + 9x3
y2
− 15x2
y3
+ 12y4
Ryxlex.<x , y> = PolynomialRing (QQ, 2 , order=' invlex ') ; Ryxlex ( pol )
6xy5
+ 12y4
+ 14x3
y3
− 15x2
y3
+ 9x3
y2
− 35x4
y + 21x5
Rlex.<x , y> = PolynomialRing (QQ, 2 , order=' lex ') ; Rlex ( pol )
21x5
− 35x4
y + 14x3
y3
+ 9x3
y2
− 15x2
y3
+ 6xy5
+ 12y4
pol . polynomial ( pol . v a r i a b l e s () [ 0 ] )
21x5
− 35yx4
+
(
14y3
+ 9y2
)
x3
− 15y3
x2
+ 6y5
x + 12y4
r e s e t () ; r=(x^2+3*x+2)/ (x^2+5*x+6) ; r ; r . numerator ( normalize=False ) ; r . \
denominator ( normalize=False ) ;
x2
+ 3 x + 2
x2 + 5 x + 6(
x2
+ 3 x + 2
)
x2
+ 5 x + 6
x=polygen (QQ, 'x') ; r=(x^2+3*x+2)/ (x^2+5*x+6) ; r
x + 1
x + 3
r e s e t () ; ( ( x^3+x^2 -x+1)/( -3*x+7*x^2 -3*x^3+7*x^4) ) . p a r t i a l _ f r a c t i o n ()
7 x + 3
29 (x2 + 1)
+
143
87 (7 x − 3)
−
1
3 x
v=(x+1) ^( -2) ; expand (v)
1
x2 + 2 x + 1
(x -1) *(x+2) /(( x+1)*x)+(x -1) /(1+x) ^2
(x + 2)(x − 1)
(x + 1)x
+
x − 1
(x + 1)
2
x=polygen (QQ, 'x') ; ( x -1) *(x+2) /(( x+1)*x)+(x -1) /(1+x) ^2
x3
+ 3x2
− 2x − 2
x3 + 2x2 + x