# # 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
# # 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
## 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()]
# # 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
# # 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 ,
# # 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)
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