* algebra/Makefile.pamphlet (all-algstrap): New.

	* algebra/strap: Update cached Lisp translation.

1 files changed, 434 insertions, 12 deletions

diff --git a/src/algebra/strap/POLYCAT-.lsp b/src/algebra/strap/POLYCAT-.lsp
index 557b4f8e..f9b376c2 100644
--- a/src/algebra/strap/POLYCAT-.lsp
+++ b/src/algebra/strap/POLYCAT-.lsp
@@ -2,8 +2,8 @@
 (/VERSIONCHECK 2) 
 
 (DEFUN |POLYCAT-;eval;SLS;1| (|p| |l| $)
-  (PROG (#0=#:G1427 #1=#:G1421 #2=#:G1428 #3=#:G1429 |lvar| #4=#:G1430
-            |e| #5=#:G1431)
+  (PROG (#0=#:G1429 #1=#:G1423 #2=#:G1430 #3=#:G1431 |lvar| #4=#:G1432
+            |e| #5=#:G1433)
     (RETURN
       (SEQ (COND
              ((NULL |l|) |p|)
@@ -121,7 +121,7 @@
         ('T (CONS 0 |l|)))))) 
 
 (DEFUN |POLYCAT-;isTimes;SU;4| (|p| $)
-  (PROG (|lv| #0=#:G1453 |v| #1=#:G1454 |l| |r|)
+  (PROG (|lv| #0=#:G1455 |v| #1=#:G1456 |l| |r|)
     (RETURN
       (SEQ (COND
              ((OR (NULL (LETT |lv|
@@ -222,7 +222,7 @@
          (CDR |lv|) (CDR |ln|) (|getShellEntry| $ 56))))) 
 
 (DEFUN |POLYCAT-;retract;SVarSet;9| (|p| $)
-  (PROG (#0=#:G1479 |q|)
+  (PROG (#0=#:G1481 |q|)
     (RETURN
       (SEQ (LETT |q|
                  (PROG2 (LETT #0# (SPADCALL |p| (|getShellEntry| $ 43))
@@ -238,7 +238,7 @@
                    ('T (|error| "Polynomial is not a single variable")))))))) 
 
 (DEFUN |POLYCAT-;retractIfCan;SU;10| (|p| $)
-  (PROG (|q| #0=#:G1487)
+  (PROG (|q| #0=#:G1489)
     (RETURN
       (SEQ (EXIT (SEQ (SEQ (LETT |q|
                                  (SPADCALL |p| (|getShellEntry| $ 43))
@@ -262,7 +262,7 @@
       (|getShellEntry| $ 62))) 
 
 (DEFUN |POLYCAT-;primitiveMonomials;SL;12| (|p| $)
-  (PROG (#0=#:G1492 |q| #1=#:G1493)
+  (PROG (#0=#:G1494 |q| #1=#:G1495)
     (RETURN
       (SEQ (PROGN
              (LETT #0# NIL |POLYCAT-;primitiveMonomials;SL;12|)
@@ -285,7 +285,7 @@
                   (GO G190) G191 (EXIT (NREVERSE0 #0#)))))))) 
 
 (DEFUN |POLYCAT-;totalDegree;SNni;13| (|p| $)
-  (PROG (#0=#:G1495 |d| |u|)
+  (PROG (#0=#:G1497 |d| |u|)
     (RETURN
       (SEQ (COND
              ((SPADCALL |p| (|getShellEntry| $ 64)) 0)
@@ -325,7 +325,7 @@
                    (EXIT |d|)))))))) 
 
 (DEFUN |POLYCAT-;totalDegree;SLNni;14| (|p| |lv| $)
-  (PROG (#0=#:G1503 |v| |w| |d| |u|)
+  (PROG (#0=#:G1505 |v| |w| |d| |u|)
     (RETURN
       (SEQ (COND
              ((SPADCALL |p| (|getShellEntry| $ 64)) 0)
@@ -382,7 +382,7 @@
       (|getShellEntry| $ 77))) 
 
 (DEFUN |POLYCAT-;allMonoms| (|l| $)
-  (PROG (#0=#:G1515 |p| #1=#:G1516)
+  (PROG (#0=#:G1517 |p| #1=#:G1518)
     (RETURN
       (SEQ (SPADCALL
                (SPADCALL
@@ -409,7 +409,7 @@
                (|getShellEntry| $ 82)))))) 
 
 (DEFUN |POLYCAT-;P2R| (|p| |b| |n| $)
-  (PROG (|w| |bj| #0=#:G1521 |i| #1=#:G1520)
+  (PROG (|w| |bj| #0=#:G1523 |i| #1=#:G1522)
     (RETURN
       (SEQ (LETT |w|
                  (SPADCALL |n| (|spadConstant| $ 23)
@@ -438,7 +438,7 @@
            (EXIT |w|))))) 
 
 (DEFUN |POLYCAT-;eq2R| (|l| |b| $)
-  (PROG (#0=#:G1525 |bj| #1=#:G1526 #2=#:G1527 |p| #3=#:G1528)
+  (PROG (#0=#:G1527 |bj| #1=#:G1528 #2=#:G1529 |p| #3=#:G1530)
     (RETURN
       (SEQ (SPADCALL
                (PROGN
@@ -488,7 +488,7 @@
                (|getShellEntry| $ 92)))))) 
 
 (DEFUN |POLYCAT-;reducedSystem;MM;20| (|m| $)
-  (PROG (#0=#:G1537 |r| #1=#:G1538 |b| #2=#:G1539 |bj| #3=#:G1540 |d|
+  (PROG (#0=#:G1539 |r| #1=#:G1540 |b| #2=#:G1541 |bj| #3=#:G1542 |d|
             |mm| |l|)
     (RETURN
       (SEQ (LETT |l| (SPADCALL |m| (|getShellEntry| $ 95))
@@ -1755,3 +1755,425 @@
                                   149 98 154 3 0 0 0 16 53 55 3 0 0 0 9
                                   36 52 1 0 145 0 156 2 0 24 0 0 186)))))
           '|lookupComplete|)) 
+
+(SETQ |$CategoryFrame|
+      (|put| '|PolynomialCategory&| '|isFunctor|
+             '(((|gcdPolynomial|
+                    ((|SparseUnivariatePolynomial| $)
+                     (|SparseUnivariatePolynomial| $)
+                     (|SparseUnivariatePolynomial| $)))
+                T (ELT $ 109))
+               ((|squareFree| ((|Factored| $) $)) T (ELT $ 165))
+               ((|squareFreePart| ($ $)) T (ELT $ 173))
+               ((|charthRoot| ((|Union| $ "failed") $)) T (ELT $ 156))
+               ((< ((|Boolean|) $ $)) T (ELT $ 186))
+               ((|convert| ((|InputForm|) $)) T (ELT $ 221))
+               ((|convert| ((|Pattern| (|Integer|)) $)) T (ELT $ 206))
+               ((|convert| ((|Pattern| (|Float|)) $)) T (ELT $ 213))
+               ((|patternMatch|
+                    ((|PatternMatchResult| (|Integer|) $) $
+                     (|Pattern| (|Integer|))
+                     (|PatternMatchResult| (|Integer|) $)))
+                T (ELT $ 192))
+               ((|patternMatch|
+                    ((|PatternMatchResult| (|Float|) $) $
+                     (|Pattern| (|Float|))
+                     (|PatternMatchResult| (|Float|) $)))
+                T (ELT $ 199))
+               ((|factor| ((|Factored| $) $)) T (ELT $ 140))
+               ((|factorPolynomial|
+                    ((|Factored| (|SparseUnivariatePolynomial| $))
+                     (|SparseUnivariatePolynomial| $)))
+                T (ELT $ 120))
+               ((|factorSquareFreePolynomial|
+                    ((|Factored| (|SparseUnivariatePolynomial| $))
+                     (|SparseUnivariatePolynomial| $)))
+                T (ELT $ 122))
+               ((|solveLinearPolynomialEquation|
+                    ((|Union| (|List| (|SparseUnivariatePolynomial| $))
+                              "failed")
+                     (|List| (|SparseUnivariatePolynomial| $))
+                     (|SparseUnivariatePolynomial| $)))
+                T (ELT $ 116))
+               ((|conditionP|
+                    ((|Union| (|Vector| $) "failed") (|Matrix| $)))
+                T (ELT $ 154))
+               ((|primitivePart| ($ $ |#4|)) T (ELT $ 183))
+               ((|content| ($ $ |#4|)) T (ELT $ 175))
+               ((|discriminant| ($ $ |#4|)) T (ELT $ 78))
+               ((|resultant| ($ $ $ |#4|)) T (ELT $ 76))
+               ((|primitiveMonomials| ((|List| $) $)) T (ELT $ 63))
+               ((|totalDegree|
+                    ((|NonNegativeInteger|) $ (|List| |#4|)))
+                T (ELT $ 74))
+               ((|totalDegree| ((|NonNegativeInteger|) $)) T
+                (ELT $ 71))
+               ((|isExpt|
+                    ((|Union| (|Record| (|:| |var| |#4|)
+                                  (|:| |exponent|
+                                       (|NonNegativeInteger|)))
+                              "failed")
+                     $))
+                T (ELT $ 47))
+               ((|isTimes| ((|Union| (|List| $) "failed") $)) T
+                (ELT $ 42))
+               ((|isPlus| ((|Union| (|List| $) "failed") $)) T
+                (ELT $ 31))
+               ((|monomial|
+                    ($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))))
+                T (ELT $ 57))
+               ((|monomial| ($ $ |#4| (|NonNegativeInteger|))) T
+                (ELT $ NIL))
+               ((|monicDivide|
+                    ((|Record| (|:| |quotient| $) (|:| |remainder| $))
+                     $ $ |#4|))
+                T (ELT $ 162))
+               ((|monomials| ((|List| $) $)) T (ELT $ 28))
+               ((|coefficient|
+                    ($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))))
+                T (ELT $ 55))
+               ((|coefficient| ($ $ |#4| (|NonNegativeInteger|))) T
+                (ELT $ 52))
+               ((|reducedSystem| ((|Matrix| |#2|) (|Matrix| $))) T
+                (ELT $ 99))
+               ((|reducedSystem|
+                    ((|Record| (|:| |mat| (|Matrix| |#2|))
+                         (|:| |vec| (|Vector| |#2|)))
+                     (|Matrix| $) (|Vector| $)))
+                T (ELT $ 106))
+               ((|reducedSystem|
+                    ((|Record| (|:| |mat| (|Matrix| (|Integer|)))
+                         (|:| |vec| (|Vector| (|Integer|))))
+                     (|Matrix| $) (|Vector| $)))
+                T (ELT $ NIL))
+               ((|reducedSystem| ((|Matrix| (|Integer|)) (|Matrix| $)))
+                T (ELT $ NIL))
+               ((|retract| (|#4| $)) T (ELT $ 59))
+               ((|retractIfCan| ((|Union| |#4| "failed") $)) T
+                (ELT $ 60))
+               ((|eval| ($ $ (|List| |#4|) (|List| $))) T (ELT $ NIL))
+               ((|eval| ($ $ |#4| $)) T (ELT $ NIL))
+               ((|eval| ($ $ (|List| |#4|) (|List| |#2|))) T
+                (ELT $ NIL))
+               ((|eval| ($ $ |#4| |#2|)) T (ELT $ NIL))
+               ((|eval| ($ $ (|List| $) (|List| $))) T (ELT $ NIL))
+               ((|eval| ($ $ $ $)) T (ELT $ NIL))
+               ((|eval| ($ $ (|Equation| $))) T (ELT $ NIL))
+               ((|eval| ($ $ (|List| (|Equation| $)))) T (ELT $ 21))
+               ((|monomial| ($ |#2| |#3|)) T (ELT $ NIL))
+               ((|coefficient| (|#2| $ |#3|)) T (ELT $ NIL))
+               ((|retract| ((|Integer|) $)) T (ELT $ NIL))
+               ((|retractIfCan| ((|Union| (|Integer|) "failed") $)) T
+                (ELT $ NIL))
+               ((|retract| ((|Fraction| (|Integer|)) $)) T (ELT $ NIL))
+               ((|retractIfCan|
+                    ((|Union| (|Fraction| (|Integer|)) "failed") $))
+                T (ELT $ NIL))
+               ((|retractIfCan| ((|Union| |#2| "failed") $)) T
+                (ELT $ NIL))
+               ((|retract| (|#2| $)) T (ELT $ NIL))
+               ((|content| (|#2| $)) T (ELT $ NIL))
+               ((|primitivePart| ($ $)) T (ELT $ 180)))
+             (|addModemap| '|PolynomialCategory&|
+                 '(|PolynomialCategory&| |#1| |#2| |#3| |#4|)
+                 '((CATEGORY |domain|
+                       (SIGNATURE |gcdPolynomial|
+                           ((|SparseUnivariatePolynomial| |#1|)
+                            (|SparseUnivariatePolynomial| |#1|)
+                            (|SparseUnivariatePolynomial| |#1|)))
+                       (SIGNATURE |squareFree|
+                           ((|Factored| |#1|) |#1|))
+                       (SIGNATURE |squareFreePart| (|#1| |#1|))
+                       (SIGNATURE |charthRoot|
+                           ((|Union| |#1| "failed") |#1|))
+                       (SIGNATURE < ((|Boolean|) |#1| |#1|))
+                       (SIGNATURE |convert| ((|InputForm|) |#1|))
+                       (SIGNATURE |convert|
+                           ((|Pattern| (|Integer|)) |#1|))
+                       (SIGNATURE |convert|
+                           ((|Pattern| (|Float|)) |#1|))
+                       (SIGNATURE |patternMatch|
+                           ((|PatternMatchResult| (|Integer|) |#1|)
+                            |#1| (|Pattern| (|Integer|))
+                            (|PatternMatchResult| (|Integer|) |#1|)))
+                       (SIGNATURE |patternMatch|
+                           ((|PatternMatchResult| (|Float|) |#1|) |#1|
+                            (|Pattern| (|Float|))
+                            (|PatternMatchResult| (|Float|) |#1|)))
+                       (SIGNATURE |factor| ((|Factored| |#1|) |#1|))
+                       (SIGNATURE |factorPolynomial|
+                           ((|Factored|
+                                (|SparseUnivariatePolynomial| |#1|))
+                            (|SparseUnivariatePolynomial| |#1|)))
+                       (SIGNATURE |factorSquareFreePolynomial|
+                           ((|Factored|
+                                (|SparseUnivariatePolynomial| |#1|))
+                            (|SparseUnivariatePolynomial| |#1|)))
+                       (SIGNATURE |solveLinearPolynomialEquation|
+                           ((|Union| (|List|
+                                      (|SparseUnivariatePolynomial|
+                                       |#1|))
+                                     "failed")
+                            (|List| (|SparseUnivariatePolynomial| |#1|))
+                            (|SparseUnivariatePolynomial| |#1|)))
+                       (SIGNATURE |conditionP|
+                           ((|Union| (|Vector| |#1|) "failed")
+                            (|Matrix| |#1|)))
+                       (SIGNATURE |primitivePart| (|#1| |#1| |#4|))
+                       (SIGNATURE |content| (|#1| |#1| |#4|))
+                       (SIGNATURE |discriminant| (|#1| |#1| |#4|))
+                       (SIGNATURE |resultant| (|#1| |#1| |#1| |#4|))
+                       (SIGNATURE |primitiveMonomials|
+                           ((|List| |#1|) |#1|))
+                       (SIGNATURE |totalDegree|
+                           ((|NonNegativeInteger|) |#1| (|List| |#4|)))
+                       (SIGNATURE |totalDegree|
+                           ((|NonNegativeInteger|) |#1|))
+                       (SIGNATURE |isExpt|
+                           ((|Union| (|Record| (|:| |var| |#4|)
+                                      (|:| |exponent|
+                                       (|NonNegativeInteger|)))
+                                     "failed")
+                            |#1|))
+                       (SIGNATURE |isTimes|
+                           ((|Union| (|List| |#1|) "failed") |#1|))
+                       (SIGNATURE |isPlus|
+                           ((|Union| (|List| |#1|) "failed") |#1|))
+                       (SIGNATURE |monomial|
+                           (|#1| |#1| (|List| |#4|)
+                                 (|List| (|NonNegativeInteger|))))
+                       (SIGNATURE |monomial|
+                           (|#1| |#1| |#4| (|NonNegativeInteger|)))
+                       (SIGNATURE |monicDivide|
+                           ((|Record| (|:| |quotient| |#1|)
+                                (|:| |remainder| |#1|))
+                            |#1| |#1| |#4|))
+                       (SIGNATURE |monomials| ((|List| |#1|) |#1|))
+                       (SIGNATURE |coefficient|
+                           (|#1| |#1| (|List| |#4|)
+                                 (|List| (|NonNegativeInteger|))))
+                       (SIGNATURE |coefficient|
+                           (|#1| |#1| |#4| (|NonNegativeInteger|)))
+                       (SIGNATURE |reducedSystem|
+                           ((|Matrix| |#2|) (|Matrix| |#1|)))
+                       (SIGNATURE |reducedSystem|
+                           ((|Record| (|:| |mat| (|Matrix| |#2|))
+                                (|:| |vec| (|Vector| |#2|)))
+                            (|Matrix| |#1|) (|Vector| |#1|)))
+                       (SIGNATURE |reducedSystem|
+                           ((|Record| (|:| |mat|
+                                       (|Matrix| (|Integer|)))
+                                      (|:| |vec|
+                                       (|Vector| (|Integer|))))
+                            (|Matrix| |#1|) (|Vector| |#1|)))
+                       (SIGNATURE |reducedSystem|
+                           ((|Matrix| (|Integer|)) (|Matrix| |#1|)))
+                       (SIGNATURE |retract| (|#4| |#1|))
+                       (SIGNATURE |retractIfCan|
+                           ((|Union| |#4| "failed") |#1|))
+                       (SIGNATURE |eval|
+                           (|#1| |#1| (|List| |#4|) (|List| |#1|)))
+                       (SIGNATURE |eval| (|#1| |#1| |#4| |#1|))
+                       (SIGNATURE |eval|
+                           (|#1| |#1| (|List| |#4|) (|List| |#2|)))
+                       (SIGNATURE |eval| (|#1| |#1| |#4| |#2|))
+                       (SIGNATURE |eval|
+                           (|#1| |#1| (|List| |#1|) (|List| |#1|)))
+                       (SIGNATURE |eval| (|#1| |#1| |#1| |#1|))
+                       (SIGNATURE |eval| (|#1| |#1| (|Equation| |#1|)))
+                       (SIGNATURE |eval|
+                           (|#1| |#1| (|List| (|Equation| |#1|))))
+                       (SIGNATURE |monomial| (|#1| |#2| |#3|))
+                       (SIGNATURE |coefficient| (|#2| |#1| |#3|))
+                       (SIGNATURE |retract| ((|Integer|) |#1|))
+                       (SIGNATURE |retractIfCan|
+                           ((|Union| (|Integer|) "failed") |#1|))
+                       (SIGNATURE |retract|
+                           ((|Fraction| (|Integer|)) |#1|))
+                       (SIGNATURE |retractIfCan|
+                           ((|Union| (|Fraction| (|Integer|)) "failed")
+                            |#1|))
+                       (SIGNATURE |retractIfCan|
+                           ((|Union| |#2| "failed") |#1|))
+                       (SIGNATURE |retract| (|#2| |#1|))
+                       (SIGNATURE |content| (|#2| |#1|))
+                       (SIGNATURE |primitivePart| (|#1| |#1|)))
+                   (|PolynomialCategory| |#2| |#3| |#4|) (|Ring|)
+                   (|OrderedAbelianMonoidSup|) (|OrderedSet|))
+                 T '|PolynomialCategory&|
+                 (|put| '|PolynomialCategory&| '|mode|
+                        '(|Mapping|
+                             (CATEGORY |domain|
+                                 (SIGNATURE |gcdPolynomial|
+                                     ((|SparseUnivariatePolynomial|
+                                       |#1|)
+                                      (|SparseUnivariatePolynomial|
+                                       |#1|)
+                                      (|SparseUnivariatePolynomial|
+                                       |#1|)))
+                                 (SIGNATURE |squareFree|
+                                     ((|Factored| |#1|) |#1|))
+                                 (SIGNATURE |squareFreePart|
+                                     (|#1| |#1|))
+                                 (SIGNATURE |charthRoot|
+                                     ((|Union| |#1| "failed") |#1|))
+                                 (SIGNATURE < ((|Boolean|) |#1| |#1|))
+                                 (SIGNATURE |convert|
+                                     ((|InputForm|) |#1|))
+                                 (SIGNATURE |convert|
+                                     ((|Pattern| (|Integer|)) |#1|))
+                                 (SIGNATURE |convert|
+                                     ((|Pattern| (|Float|)) |#1|))
+                                 (SIGNATURE |patternMatch|
+                                     ((|PatternMatchResult| (|Integer|)
+                                       |#1|)
+                                      |#1| (|Pattern| (|Integer|))
+                                      (|PatternMatchResult| (|Integer|)
+                                       |#1|)))
+                                 (SIGNATURE |patternMatch|
+                                     ((|PatternMatchResult| (|Float|)
+                                       |#1|)
+                                      |#1| (|Pattern| (|Float|))
+                                      (|PatternMatchResult| (|Float|)
+                                       |#1|)))
+                                 (SIGNATURE |factor|
+                                     ((|Factored| |#1|) |#1|))
+                                 (SIGNATURE |factorPolynomial|
+                                     ((|Factored|
+                                       (|SparseUnivariatePolynomial|
+                                        |#1|))
+                                      (|SparseUnivariatePolynomial|
+                                       |#1|)))
+                                 (SIGNATURE
+                                     |factorSquareFreePolynomial|
+                                     ((|Factored|
+                                       (|SparseUnivariatePolynomial|
+                                        |#1|))
+                                      (|SparseUnivariatePolynomial|
+                                       |#1|)))
+                                 (SIGNATURE
+                                     |solveLinearPolynomialEquation|
+                                     ((|Union|
+                                       (|List|
+                                        (|SparseUnivariatePolynomial|
+                                         |#1|))
+                                       "failed")
+                                      (|List|
+                                       (|SparseUnivariatePolynomial|
+                                        |#1|))
+                                      (|SparseUnivariatePolynomial|
+                                       |#1|)))
+                                 (SIGNATURE |conditionP|
+                                     ((|Union| (|Vector| |#1|)
+                                       "failed")
+                                      (|Matrix| |#1|)))
+                                 (SIGNATURE |primitivePart|
+                                     (|#1| |#1| |#4|))
+                                 (SIGNATURE |content| (|#1| |#1| |#4|))
+                                 (SIGNATURE |discriminant|
+                                     (|#1| |#1| |#4|))
+                                 (SIGNATURE |resultant|
+                                     (|#1| |#1| |#1| |#4|))
+                                 (SIGNATURE |primitiveMonomials|
+                                     ((|List| |#1|) |#1|))
+                                 (SIGNATURE |totalDegree|
+                                     ((|NonNegativeInteger|) |#1|
+                                      (|List| |#4|)))
+                                 (SIGNATURE |totalDegree|
+                                     ((|NonNegativeInteger|) |#1|))
+                                 (SIGNATURE |isExpt|
+                                     ((|Union|
+                                       (|Record| (|:| |var| |#4|)
+                                        (|:| |exponent|
+                                         (|NonNegativeInteger|)))
+                                       "failed")
+                                      |#1|))
+                                 (SIGNATURE |isTimes|
+                                     ((|Union| (|List| |#1|) "failed")
+                                      |#1|))
+                                 (SIGNATURE |isPlus|
+                                     ((|Union| (|List| |#1|) "failed")
+                                      |#1|))
+                                 (SIGNATURE |monomial|
+                                     (|#1| |#1| (|List| |#4|)
+                                      (|List| (|NonNegativeInteger|))))
+                                 (SIGNATURE |monomial|
+                                     (|#1| |#1| |#4|
+                                      (|NonNegativeInteger|)))
+                                 (SIGNATURE |monicDivide|
+                                     ((|Record| (|:| |quotient| |#1|)
+                                       (|:| |remainder| |#1|))
+                                      |#1| |#1| |#4|))
+                                 (SIGNATURE |monomials|
+                                     ((|List| |#1|) |#1|))
+                                 (SIGNATURE |coefficient|
+                                     (|#1| |#1| (|List| |#4|)
+                                      (|List| (|NonNegativeInteger|))))
+                                 (SIGNATURE |coefficient|
+                                     (|#1| |#1| |#4|
+                                      (|NonNegativeInteger|)))
+                                 (SIGNATURE |reducedSystem|
+                                     ((|Matrix| |#2|) (|Matrix| |#1|)))
+                                 (SIGNATURE |reducedSystem|
+                                     ((|Record|
+                                       (|:| |mat| (|Matrix| |#2|))
+                                       (|:| |vec| (|Vector| |#2|)))
+                                      (|Matrix| |#1|) (|Vector| |#1|)))
+                                 (SIGNATURE |reducedSystem|
+                                     ((|Record|
+                                       (|:| |mat|
+                                        (|Matrix| (|Integer|)))
+                                       (|:| |vec|
+                                        (|Vector| (|Integer|))))
+                                      (|Matrix| |#1|) (|Vector| |#1|)))
+                                 (SIGNATURE |reducedSystem|
+                                     ((|Matrix| (|Integer|))
+                                      (|Matrix| |#1|)))
+                                 (SIGNATURE |retract| (|#4| |#1|))
+                                 (SIGNATURE |retractIfCan|
+                                     ((|Union| |#4| "failed") |#1|))
+                                 (SIGNATURE |eval|
+                                     (|#1| |#1| (|List| |#4|)
+                                      (|List| |#1|)))
+                                 (SIGNATURE |eval|
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+                                 (SIGNATURE |eval|
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+                                 (SIGNATURE |eval|
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+                                 (SIGNATURE |eval|
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+                                      (|List| (|Equation| |#1|))))
+                                 (SIGNATURE |monomial|
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+                                 (SIGNATURE |retract|
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