Esempi in Python per WordPolyRing

Esempio n. 1

File: word_simple.py Progetto: zourzouvillys/java-algebra-system

#
# jython examples for jas.
# $Id$
#

#from java.lang import System

from jas import WordRing, WordPolyRing, WordPolyIdeal
from jas import terminate, startLog
from jas import QQ, ZZ, GF, ZM

# non-commutative polynomial examples: simple test

r = WordPolyRing(QQ(), "x,y")
print "WordPolyRing: " + str(r)
print

[one, x, y] = r.gens()
print "one = " + str(one)
print "x = " + str(x)
print "y = " + str(y)
print

f1 = x * y - (1, 10)
f2 = y * x + x + y

print "f1 = " + str(f1)
print "f2 = " + str(f2)
print

c1 = f1 * f2

Esempio n. 2

#
# jython examples for jas.
# $Id$
#

#from java.lang import System

from jas import WordRing, WordPolyRing, WordPolyIdeal, PolyRing, SolvPolyRing
from jas import terminate, startLog
from jas import QQ, ZZ, GF, ZM

# non-commutative polynomial examples: solvable polynomials example

#r = WordPolyRing(QQ(),"a,b,e1,e2,e3");
r = WordPolyRing(QQ(), "a,b,e,f,g")
print "WordPolyRing: " + str(r)
print

[one, a, b, e, f, g] = r.gens()
print "one = " + str(one)
print "a = " + str(a)
print "b = " + str(b)
print "e = " + str(e)
print "f = " + str(f)
print "g = " + str(g)
print

r1 = g * e - (e * g - e)
r2 = g * f - (f * g - f)
r3 = e * a - a * e
r4 = e * b - b * e

Esempio n. 3

#
# jython examples for jas.
# $Id$
#

#from java.lang import System

from jas import WordRing, WordPolyRing, WordPolyIdeal
from jas import terminate, startLog
from jas import QQ, ZZ, GF, ZM

# non-commutative polynomial examples: simple test

r = WordPolyRing(QQ(),"x,y");
print "WordPolyRing: " + str(r);
print;

[one,x,y] = r.gens();
print "one = " + str(one);
print "x = " + str(x);
print "y = " + str(y);
print;

f1 = x*y - (1,10);
f2 = y*x + x + y;

print "f1 = " + str(f1);
print "f2 = " + str(f2);
print;

c1 = f1 * f2;

Esempio n. 4

## 2 z_2+6ay_2+20 y_2^3+2c \&
## 3 z_1^2+y_1^2+b \&
## 3z_2^2+y_2^2+b \&
## \end{Equations}
## \end{PossoExample}

#from java.lang import System

from jas import WordRing, WordPolyRing, WordPolyIdeal, PolyRing, SolvPolyRing, RingElem
from jas import terminate, startLog
from jas import QQ, ZZ, GF, ZM, WRC

# Hawes & Gibson example 2
# rational function coefficients

r = WordPolyRing(PolyRing(ZZ(), "a, c, b", PolyRing.lex), "y2, y1, z1, z2, x")
print "Ring: " + str(r)
print

one, a, c, b, y2, y1, z1, z2, x = r.gens()

p1 = x + 2 * y1 * z1 + 3 * a * y1**2 + 5 * y1**4 + 2 * c * y1
p2 = x + 2 * y2 * z2 + 3 * a * y2**2 + 5 * y2**4 + 2 * c * y2
p3 = 2 * z2 + 6 * a * y2 + 20 * y2**3 + 2 * c
p4 = 3 * z1**2 + y1**2 + b
p5 = 3 * z2**2 + y2**2 + b

F = [p1, p2, p3, p4, p5]

# make all variables commute
cm = [RingElem(q) for q in r.ring.commute()]

Esempio n. 5

File: word_exterior.py Progetto: rjolly/jas

#
# jython examples for jas.
# $Id$
#

from java.lang import System

from jas import WordRing, WordPolyRing, WordPolyIdeal
from jas import terminate, startLog
from jas import QQ, ZZ, GF, ZM

# exterior calculus example
# Hartley and Tuckey, 1993,
# GB in Clifford and Grassmann algebras

r = WordPolyRing(QQ(), "a,b,c,f,g,h,u,v,w,x,y,z");
#r = WordPolyRing(ZZ(), "a,b,c,f,g,h,u,v,w,x,y,z");
print "WordPolyRing: " + str(r);
print;

one,a,b,c,f,g,h,u,v,w,x,y,z = r.gens();
print "a = %s" % a;
print "z = %s" % z;
print;

# exterior algebra relations
rs = [
  b * a   - a * b ,
  c * a   - a * c ,
  f * a   - a * f ,
  g * a   - a * g ,

Esempio n. 6

File: word_hawes2.py Progetto: rjolly/jas

## 2 z_2+6ay_2+20 y_2^3+2c \&
## 3 z_1^2+y_1^2+b \&
## 3z_2^2+y_2^2+b \&
## \end{Equations}
## \end{PossoExample}

#from java.lang import System

from jas import WordRing, WordPolyRing, WordPolyIdeal, PolyRing, SolvPolyRing, RingElem
from jas import terminate, startLog
from jas import QQ, ZZ, GF, ZM, WRC

# Hawes & Gibson example 2
# rational function coefficients

r = WordPolyRing( PolyRing(ZZ(),"a, c, b",PolyRing.lex), "y2, y1, z1, z2, x" );
print "Ring: " + str(r);
print;

one,a,c,b,y2,y1,z1,z2,x = r.gens();

p1 = x + 2 * y1 * z1 + 3 * a * y1**2 + 5 * y1**4 + 2 * c * y1;
p2 = x + 2 * y2 * z2 + 3 * a * y2**2 + 5 * y2**4 + 2 * c * y2;
p3 = 2 * z2 + 6 * a * y2 + 20 * y2**3 + 2 * c; 
p4 = 3 * z1**2 + y1**2 + b;
p5 = 3 * z2**2 + y2**2 + b; 

F = [p1,p2,p3,p4,p5];

# make all variables commute
cm = [ RingElem(q) for q in r.ring.commute() ];

Esempio n. 7

File: word_evans.py Progetto: siwiwit/java-algebra-system

#
# jython examples for jas.
# $Id$
#

# from java.lang import System

from jas import WordRing, WordPolyRing, WordPolyIdeal
from jas import terminate, startLog
from jas import QQ, ZZ, GF, ZM

# non-commutative polynomial examples: evans example

r = WordPolyRing(QQ(), "x,y,z")
print "WordPolyRing: " + str(r)
print

[one, x, y, z] = r.gens()
print "one = " + str(one)
print "x = " + str(x)
print "y = " + str(y)
print "z = " + str(z)
print

f1 = x * y - z
f2 = y * z + 2 * x + z
f3 = y * z + x

print "f1 = " + str(f1)
print "f2 = " + str(f2)
print "f3 = " + str(f3)

Esempio n. 8

File: word_solvable_trans.py Progetto: rjolly/jas

#
# jython examples for jas.
# $Id$
#

#from java.lang import System

from jas import WordRing, WordPolyRing, WordPolyIdeal, PolyRing, SolvPolyRing
from jas import terminate, startLog
from jas import QQ, ZZ, GF, ZM

# non-commutative polynomial examples: solvable polynomials example

r = WordPolyRing(QQ(),"a,b,e1,e2,e3");
print "WordPolyRing: " + str(r);
print;

[one,a,b,e1,e2,e3] = r.gens();
print "one = " + str(one);
print "a = " + str(a);
print "b = " + str(b);
print "e1 = " + str(e1);
print "e2 = " + str(e2);
print "e3 = " + str(e3);
print;

r1 = e3 * e1 - (e1 * e3 - e1);
r2 = e3 * e2 - (e2 * e3 - e2);
r3 = e1 * a - a * e1;
r4 = e1 * b - b * e1;
r5 = e2 * a - a * e2;

Esempio n. 9

#
# jruby examples for jas.
# $Id$
#

#from java.lang import System

from jas import WordRing, WordPolyRing, WordPolyIdeal
from jas import terminate, startLog
from jas import QQ, ZZ, GF, ZM, WRC

# exterior calculus example
# Hartley and Tuckey, 1993,
# GB in Clifford and Grassmann algebras

r = WordPolyRing(QQ(), "a,b,c,f,g,h,u,v,w,x,y,z");
print "WordPolyRing: " + str(r);
print;

one,a,b,c,f,g,h,u,v,w,x,y,z = r.gens();
print "a = %s" % a;
print "z = %s" % z;
print;

# exterior algebra relations
rs = [
  b * a   - a * b ,
  c * a   - a * c ,
  f * a   - a * f ,
  g * a   - a * g ,
  h * a   - a * h ,

Esempio n. 10

#
# jython examples for jas.
# $Id$
#

#from java.lang import System

from jas import WordRing, WordPolyRing, WordPolyIdeal
from jas import terminate, startLog
from jas import QQ, ZZ, GF, ZM

# non-commutative polynomial examples: evans example

r = WordPolyRing(QQ(), "x,y,z")
print "WordPolyRing: " + str(r)
print

[one, x, y, z] = r.gens()
print "one = " + str(one)
print "x = " + str(x)
print "y = " + str(y)
print "z = " + str(z)
print

f1 = x * y - z
f2 = y * z + 2 * x + z
f3 = y * z + x

print "f1 = " + str(f1)
print "f2 = " + str(f2)
print "f3 = " + str(f3)

Esempio n. 11

File: word_solvable.py Progetto: rjolly/jas

#
# jython examples for jas.
# $Id$
#

# from java.lang import System

from jas import WordRing, WordPolyRing, WordIdeal, PolyRing, SolvPolyRing
from jas import terminate, startLog
from jas import QQ, ZZ, GF, ZM

# non-commutative polynomial examples: solvable polynomials example

# r = WordPolyRing(QQ(),"a,b,e1,e2,e3");
r = WordPolyRing(QQ(), "a,b,e,f,g")
print "WordPolyRing: " + str(r)
print

[one, a, b, e, f, g] = r.gens()
print "one = " + str(one)
print "a = " + str(a)
print "b = " + str(b)
print "e = " + str(e)
print "f = " + str(f)
print "g = " + str(g)
print

r1 = g * e - (e * g - e)
r2 = g * f - (f * g - f)
r3 = e * a - a * e
r4 = e * b - b * e

Esempio n. 12

File: word_exterior.py Progetto: zourzouvillys/java-algebra-system

#
# jython examples for jas.
# $Id$
#

from java.lang import System

from jas import WordRing, WordPolyRing, WordPolyIdeal
from jas import terminate, startLog
from jas import QQ, ZZ, GF, ZM

# exterior calculus example
# Hartley and Tuckey, 1993,
# GB in Clifford and Grassmann algebras

r = WordPolyRing(QQ(), "a,b,c,f,g,h,u,v,w,x,y,z")
#r = WordPolyRing(ZZ(), "a,b,c,f,g,h,u,v,w,x,y,z");
print "WordPolyRing: " + str(r)
print

one, a, b, c, f, g, h, u, v, w, x, y, z = r.gens()
print "a = %s" % a
print "z = %s" % z
print

# exterior algebra relations
rs = [
    b * a - a * b, c * a - a * c, f * a - a * f, g * a - a * g, h * a - a * h,
    u * a - a * u, v * a - a * v, w * a - a * w, x * a - a * x, y * a - a * y,
    z * a - a * z, c * b - b * c, f * b - b * f, g * b - b * g, h * b - b * h,
    u * b - b * u, v * b - b * v, w * b - b * w, x * b - b * x, y * b - b * y,

Esempio n. 13

File: freealg-C_417_X.py Progetto: rjolly/jas

from java.lang import System

from jas import WordRing, WordPolyRing, WordIdeal
from jas import terminate, startLog
from jas import QQ, ZZ, GF, ZM

# non-commutative polynomial examples: C_4_1_7_X example

#r = WordPolyRing(QQ,"x4,x3,x2,x1");
#r = WordPolyRing(GF(19),"x4,x3,x2,x1");

#r = WordPolyRing(QQ(),"x1,x2,x3,x4");
#r = WordPolyRing(ZZ(),"x1,x2,x3,x4");
#r = WordPolyRing(GF(19),"x1,x2,x3,x4");
#r = WordPolyRing(GF(32003),"x1,x2,x3,x4");
r = WordPolyRing(GF(2**29-3),"x1,x2,x3,x4");
#r = WordPolyRing(GF(2**63-25),"x1,x2,x3,x4");
#r = WordPolyRing(GF(170141183460469231731687303715884105727),"x1,x2,x3,x4");
#r = WordPolyRing(GF(259117086013202627776246767922441530941818887553125427303974923161874019266586362086201209516800483406550695241733194177441689509238807017410377709597512042313066624082916353517952311186154862265604547691127595848775610568757931191017711408826252153849035830401185072116424747461823031471398340229288074545677907941037288235820705892351068433882986888616658650280927692080339605869308790500409503709875902119018371991620994002568935113136548829739112656797303241986517250116412703509705427773477972349821676443446668383119322540099648994051790241624056519054483690809616061625743042361721863339415852426431208737266591962061753535748892894599629195183082621860853400937932839420261866586142503251450773096274235376822938649407127700846077124211823080804139298087057504713825264571448379371125032081826126566649084251699453951887789613650248405739378594599444335231188280123660406262468609212150349937584782292237144339628858485938215738821232393687046160677362909315071),"x1,x2,x3,x4");
print "WordPolyRing: " + str(r);
print;


#one,x4,x3,x2,x1 = r.gens();
one,x1,x2,x3,x4 = r.gens();
print "one = " + str(one);
print "x4 = " + str(x4);
print "x3 = " + str(x3);
print "x2 = " + str(x2);
print "x1 = " + str(x1);
print;

Esempio n. 14

File: freealg-C_417_X.py Progetto: zourzouvillys/java-algebra-system

from java.lang import System

from jas import WordRing, WordPolyRing, WordIdeal
from jas import terminate, startLog
from jas import QQ, ZZ, GF, ZM

# non-commutative polynomial examples: C_4_1_7_X example

#r = WordPolyRing(QQ,"x4,x3,x2,x1");
#r = WordPolyRing(GF(19),"x4,x3,x2,x1");

#r = WordPolyRing(QQ(),"x1,x2,x3,x4");
#r = WordPolyRing(ZZ(),"x1,x2,x3,x4");
#r = WordPolyRing(GF(19),"x1,x2,x3,x4");
#r = WordPolyRing(GF(32003),"x1,x2,x3,x4");
r = WordPolyRing(GF(2**29 - 3), "x1,x2,x3,x4")
#r = WordPolyRing(GF(2**63-25),"x1,x2,x3,x4");
#r = WordPolyRing(GF(170141183460469231731687303715884105727),"x1,x2,x3,x4");
#r = WordPolyRing(GF(259117086013202627776246767922441530941818887553125427303974923161874019266586362086201209516800483406550695241733194177441689509238807017410377709597512042313066624082916353517952311186154862265604547691127595848775610568757931191017711408826252153849035830401185072116424747461823031471398340229288074545677907941037288235820705892351068433882986888616658650280927692080339605869308790500409503709875902119018371991620994002568935113136548829739112656797303241986517250116412703509705427773477972349821676443446668383119322540099648994051790241624056519054483690809616061625743042361721863339415852426431208737266591962061753535748892894599629195183082621860853400937932839420261866586142503251450773096274235376822938649407127700846077124211823080804139298087057504713825264571448379371125032081826126566649084251699453951887789613650248405739378594599444335231188280123660406262468609212150349937584782292237144339628858485938215738821232393687046160677362909315071),"x1,x2,x3,x4");
print "WordPolyRing: " + str(r)
print

#one,x4,x3,x2,x1 = r.gens();
one, x1, x2, x3, x4 = r.gens()
print "one = " + str(one)
print "x4 = " + str(x4)
print "x3 = " + str(x3)
print "x2 = " + str(x2)
print "x1 = " + str(x1)
print