Changeset 4387

Timestamp:

2016-06-07T09:24:32-07:00 (8 years ago)

Author:

Marek Rychlik

Message:

 

Location:

branches/f4grobner

Files:

• 5am-buchberger.lisp (modified) (1 diff)
• 5am-division.lisp (modified) (4 diffs)
• rational-field.lisp (modified) (1 diff)

branches/f4grobner/5am-buchberger.lisp

@@ -102 +102 @@
     (&body)))
     
+#+nil
+(test buchberger-advanced-preliminary
+  (with-fixture buchberger-advanced-context ()
+    (print (poly->string (elt gb 0)))
+    (print (poly->string (elt gb 6)))))
+    
+
+#+nil
+(test buchberger-advanced-partial
+  (with-fixture buchberger-advanced-context ()
+    (loop 
+       for i from 0 below (length gb)
+       do
+         (loop 
+            for j from (1+ i) below (length gb)
+            do
+              (is (universal-zerop (second (multiple-value-list (poly-pseudo-divide (s-polynomial (elt gb i) (elt gb j)) gb))))
+                  "Failed with I=~S, J=~S~%" I J)))))
+
+#-nil
 (test buchberger-advanced
   "Buchberger algorithm - advanced case"
   (with-fixture buchberger-advanced-context ()
-    (is-true (grobner-test gb fl))
-    ;;(is (every #'universal-equalp (buchberger fl) gb))
+    ;;(is-true (grobner-test gb fl))
+    (is (every #'universal-equalp (buchberger fl) gb))
     ;;(is (every #'universal-equalp (parallel-buchberger fl) gb))
     ))

branches/f4grobner/5am-division.lisp

@@ -39 +39 @@
 
 (defpackage #:5am-division
-  (:use :cl :it.bese.fiveam :monom :polynomial :infix :symbolic-polynomial :division :ring))
+  (:use :cl :it.bese.fiveam :copy :monom :polynomial :infix :symbolic-polynomial :division :ring))
 
 (in-package :5am-division)
@@ -62 +62 @@
          (fl (cdr (string->poly "[x+y,x-2*y]" '(x y))))
          (quotients (cdr (string->poly "[x-y,0]" '(x y))))
-         (one (make-instance 'integer-ring :value 1)))
+         (one (make-instance 'rational-field :value 1)))
     (&body)))
 
@@ -73 +73 @@
     )
   )
+
+;; Maxima
+;;poly_normal_form(3*x^3*y+2*z, [x^2*y+x,x-y^2-z^3],[x,y,z]);
+;;Result: (-3*z^6)-6*y^2*z^3+2*z-3*y^4
+(test normal-form-simple 
+  (let ((vars '(x y z)))
+    (is (universal-equalp (normal-form (string->poly "3*x^3*y+2*z" vars)
+                                       (cdr (string->poly "[x^2*y+x,x-y^2-z^3]" vars)))
+                          (string->poly "(-3*z^6)-6*y^2*z^3+2*z-3*y^4" vars)))))
 
 (test normal-form-easy
@@ -98 +107 @@
 
 
+;; Check if a set of generators satisfies the Buchberger criterion
+;; The example is the Enneper surface ideal. Run this in Maxima to
+;; obtain the Grobner basis:
+;;   poly_grobner([x-3*u-3*u*v^2+u^3,y-3*v-3*u^2*v+v^3,z-3*u^2+3*v^2],[u,v,x,y,z]);
+(def-fixture buchberger-criterion-context ()
+  (let ((fl (cdr (string->poly "[x-3*u-3*u*v^2+u^3,y-3*v-3*u^2*v+v^3,z-3*u^2+3*v^2]" '(u v x y z))))
+        (gb (cdr (string->poly "[x-3*u*v^2+u^3-3*u,y+v^3-3*u^2*v-3*v,z+3*v^2-3*u^2,
+       (-u*z)-3*x+6*u*v^2+9*u,(-v*z)+y-2*v^3-3*v,z^2+6*v^2*z-9*z-9*v*y+9*u*x,
+       4*u*v*z-3*u*y+3*v*x,2*u*z^2+6*x*z-18*u*z-9*u*v*y+9*v^2*x,
+       (-8*u*z^3)-24*x*z^2+72*u*z^2-36*v^2*x*z+27*u*y^2-27*v*x*y,
+       z^3+18*v^2*z^2-18*z^2-54*v*y*z+54*v^2*z+81*z+27*y^2-27*x^2,
+       (-4*z^4)+48*z^3-108*v*y*z^2+108*z^2+135*y^2*z+324*v*y*z+108*x^2*z
+               -1296*v^2*z-1944*z-243*v^2*y^2-648*y^2+243*v^2*x^2+648*x^2,
+       8*v*z^3-9*y*z^2+72*v*z^2+54*v^2*y*z-27*y*z-27*v*y^2+27*v*x^2,
+       (-8*v*z^4)+12*y*z^3-96*v*z^3-216*v*z^2-135*v*y^2*z+324*y*z-27*v*x^2*z
+                 +81*y^3+81*v*y^2-81*x^2*y-81*v*x^2,
+       (-64*v*z^6)+120*y*z^5-1152*v*z^5+288*y*z^4-5184*v*z^4-648*v*y^2*z^3
+                  -216*y*z^3+6912*v*z^3+81*y^3*z^2-9720*v*y^2*z^2
+                  -1539*x^2*y*z^2+31104*y*z^2+62208*v*z^2+8505*y^3*z
+                  +46656*v*y^2*z-8505*x^2*y*z-93312*y*z+729*v*y^4-23328*y^3
+                  -1458*v*x^2*y^2-23328*v*y^2+23328*x^2*y+729*v*x^4
+                  +23328*v*x^2,
+       8*z^6-72*z^5+648*v*y*z^4-648*z^4-945*y^2*z^3+5184*v*y*z^3-189*x^2*z^3
+            +5832*z^3+972*y^2*z^2+17496*v*y*z^2-2430*x^2*z^2+8748*v*y^3*z
+            -19683*y^2*z+2187*x^2*z-5103*y^4-4374*v*y^3+5832*x^2*y^2
+            +4374*v*x^2*y-729*x^4,
+       8*z^7-48*z^6+648*v*y*z^5-864*z^5-945*y^2*z^4+5832*v*y*z^4-189*x^2*z^4
+            +3888*z^4+81*y^2*z^3+17496*v*y*z^3-2997*x^2*z^3+17496*z^3
+            +8748*v*y^3*z^2-16767*y^2*z^2+17496*v*y*z^2-5103*x^2*z^2
+            -5103*y^4*z+5832*x^2*y^2*z-6561*y^2*z-729*x^4*z+6561*x^2*z
+            -2187*y^4+4374*x^2*y^2-2187*x^4,
+       64*z^9-10368*z^7+1296*y^2*z^6-1296*x^2*z^6-34992*y^2*z^5-34992*x^2*z^5
+             +419904*z^5+174960*y^2*z^4-174960*x^2*z^4-10935*y^4*z^3
+             -56862*x^2*y^2*z^3+314928*y^2*z^3-10935*x^4*z^3+314928*x^2*z^3
+             +118098*y^4*z^2-118098*x^4*z^2+59049*y^4*z-118098*x^2*y^2*z
+             +59049*x^4*z+19683*y^6-59049*x^2*y^4+59049*x^4*y^2-19683*x^6]" '(u v x y z)))))
+    (&body)))
+    
+#+nil
+(test buchberger-criterion-preliminary
+  (with-fixture buchberger-criterion-context ()
+    (print (poly->string (elt gb 0)))
+    (print (poly->string (elt gb 6)))))
+    
+
+#+nil
+(test buchberger-containment
+  "Check ideal containment"
+  (with-fixture buchberger-criterion-context 
+      ()
+    (let ((fl-copy (mapcar #'copy-instance fl))
+          (gb-copy (mapcar #'copy-instance gb)))
+      (loop 
+         for i from 0 below (length fl)
+         do
+           (is (universal-zerop (normal-form (elt fl i) gb))
+               "Failed with I=~S~%" I))
+      ;; GB should not change in the process
+      (is (universal-equalp gb gb-copy))
+      (is (universal-equalp fl fl-copy)))))
+
+#+nil
+(test buchberger-criterion-full
+  (with-fixture buchberger-criterion-context 
+      ()
+    (loop 
+       for i from 0 below (length gb)
+       do
+         (loop 
+            for j from (1+ i) below (length gb)
+            do
+              (is (universal-zerop (normal-form (s-polynomial (elt gb i) (elt gb j)) gb))
+                  "Failed with I=~S, J=~S~%" I J)))))
+
+#+nil
+(test buchberger-criterion
+  "Buchberger criterion"
+  (with-fixture buchberger-advanced-context ()
+    (is-true (grobner-test gb fl))
+    )
+  )
+
+
 (run! 'division-suite)
 (format t "All tests done!~%")

branches/f4grobner/rational-field.lisp

@@ -105 +105 @@
   (copy-instance *rational-field-unit*))
 
-
-(defmethod universal-ezgcd ((object rational-field) (other rational-field))
-  (values (copy-instance *rational-field-unit*)
-          (copy-instance object)
-          (copy-instance other)))