Populate Nemo p-adic integer arithmetic

src/algebra/Makefile.in

@@ -395,14 +395,14 @@ GUESSLIST= SMPEXPR FAMR2 NEWTON UFPS GOPT GUESSF1 GUESSP1\
            RECOP STNSR GUESS GUESSEB  GUESSINT GUESSF GUESSP GUESSPI GUESSAN
 
 ifdef JULIA_WRAP_SO_TARGET
-JULIALIST = INECF INPADICZ JARBPR JCF32 JCF32VEC JCF32MAT JCF32SMA \
+JULIALIST = EXPADICZ INECF JARBPR JCF32 JCF32VEC JCF32MAT JCF32SMA \
             JCF64 JCF64MAT JCF64MTF JCF64SMA JCF64VEC JCFSF JCFLOAT JCF32LA \
             JCF64LA JCRING JDFRAME JDRAW JF32 JF32AF JF32VEC JF32VEC2 JF32MAT \
             JF32SMAT JF64 JF64AF JF64MAT JF64MTF JF32SF JF64SF JF32SF2 JF64SF2 \
-		  JF64SMAT JF64VEC JF64VEC2 JFLOAT JFSF JFSF2 JI64 JI64VEC JMATCAT \
-		  JMATRIX JMFLOAT JMTYPE JOBJECT JOBAGG JOBBOOL JOBBINT JOBCF32 JOBCF64 \
-		  JOBDICT JOBDLINK JOBF32 JOBF64 JOBI64 JOBPAIR JOBRING JOBTPLE JOBTYPE \
-		  JPLOT JRING JF32LA JF64LA JSTRU JSYM JUF JTYPE JVECCAT JVECTOR JVECTOR2 \
+		    JF64SMAT JF64VEC JF64VEC2 JFLOAT JFSF JFSF2 JI64 JI64VEC JMATCAT \
+		    JMATRIX JMFLOAT JMTYPE JOBJECT JOBAGG JOBBOOL JOBBINT JOBCF32 JOBCF64 \
+		    JOBDICT JOBDLINK JOBF32 JOBF64 JOBI64 JOBPAIR JOBRING JOBTPLE JOBTYPE \
+		    JPLOT JRING JF32LA JF64LA JSTRU JSYM JUF JTYPE JVECCAT JVECTOR JVECTOR2 \
             NACF NACFS NAN NACB NARB NCB NCF NCRING NECF NFF NFR NFRAC NPADICC \
             NINT NMLP NMP NPADICZ NPF NRB NRF NRING NTYPE NULP NUP NZMOD
 JULIACATLIST = JARBPR JCRING JMATCAT JMFLOAT JMTYPE JOBAGG JOBRING JOBTYPE \

src/algebra/exposed.lsp

@@ -466,6 +466,8 @@
   (|Evalable| . EVALAB)
   (|ExpressionSpace| . ES)
   (|ExpressionSpace2| . ESC2)
+  (|ExtendedNMPAdicInteger| . EXPADICZ)
+  (|ExtendedNMPAdicRational| . EXPADICQ)
   (|ExtensibleLinearAggregate| . ELAGG)
   (|ExtensionField| . XF)
   (|Field| . FIELD)
@@ -773,7 +775,6 @@
   (|InnerNormalBasisFieldFunctions| . INBFF)
   (|InnerNumericEigenPackage| . INEP)
   (|InnerNumericFloatSolvePackage| . INFSP)
-  (|InnerPAdicInteger| . IPADICZ)
   (|InnerPolySign| . INPSIGN)
   (|InnerPolySum| . ISUMP)
   (|InnerPrimeField| . IPF)

src/algebra/jnball.spad

@@ -594,7 +594,7 @@ NMComplexBall() == NMAcbField(256)
 ++ Keywords: arbitrary precision, floating point number, real
 ++ Description:
 ++  \spadtype{NMRealField} implements arbitrary precision ball
-++  arithmetic using the NM JL package.
+++  arithmetic using the Nemo Julia package.
 ++ Reference: https://nemocas.github.io/NM.jl/stable/
 NMRealField() : Exports == Implementation where
   PI        ==> PositiveInteger
@@ -890,7 +890,7 @@ NMRealField() : Exports == Implementation where
 ++ Keywords: arbitrary precision, floating point  number, complex
 ++ Description:
 ++ \spadtype{NMComplexField} implements arbitrary precision ball
-++ arithmetic using the NM JL package.
+++ arithmetic using the Nemo Julia package.
 ++ Reference: https://nemocas.github.io/NM.jl/stable/
 NMComplexField() : Exports == Implementation where
   JI64      ==> JLInt64

src/algebra/jnemo.spad

@@ -528,7 +528,7 @@ NMIntegerMod(p : PositiveInteger) : Exports == Implementation where
 ++ Date Created: Feb. 2024
 ++ Description:
 ++  This domain allows the manipulation of NM prime field
-++  elements using the NM JL package (FLINT based).
+++  elements using the Nemo Julia package (FLINT based).
 ++ https://flintlib.org/
 NMPrimeField(p : PositiveInteger) : Exports == Implementation where
   PI        ==> PositiveInteger
@@ -644,7 +644,7 @@ NMPrimeField(p : PositiveInteger) : Exports == Implementation where
 ++ Date Created: Feb. 2024
 ++ Description:
 ++  This domain allows the manipulation of NM Galois field
-++  of p^n elements using the NM JL package (FLINT based).
+++  of p^n elements using the Nemo Julia package (FLINT based).
 ++ https://flintlib.org/
 NMFiniteField(p : PositiveInteger, n: PositiveInteger) : Exports == Implementation where
   PI        ==> PositiveInteger

src/algebra/jnpadic.spad

@@ -8,14 +8,13 @@
 ++ Keywords: p-adic, completion
 ++ Examples:
 ++ References:
-++ Description: This is the catefory of stream-based representations of
+++ Description: This is the category representations of
 ++   the p-adic integers.
 NMPadicIntegerCategory(p) : Category == Definition where
   p     :   NMInteger
   NINT  ==> NMInteger
   I     ==> Integer
   NNI   ==> NonNegativeInteger
-
   Definition ==> Join(EuclideanDomain, CharacteristicZero) with
     --digits : % -> ST I
     --  ++ \spad{digits(x)} returns a stream of p-adic digits of x.
@@ -43,7 +42,7 @@ NMPadicIntegerCategory(p) : Category == Definition where
     --  ++ \spad{root(f, a)} returns a root of the polynomial \spad{f}.
     --  ++ Argument \spad{a} must be a root of \spad{f} \spad{(mod p)}.
 
-)abbrev domain INPADICZ InnerNMPadicInteger
+)abbrev domain EXPADICZ ExtendedNMPadicInteger
 ++ Author: Vanuxem Grégory
 ++ Date Created: 1 February 2025
 ++ Basic Operations:
@@ -56,7 +55,7 @@ NMPadicIntegerCategory(p) : Category == Definition where
 ++ References:
 ++ Description:
 ++   This domain implements Zp, the p-adic completion of the integers.
-InnerNMPadicInteger(p : NMInteger, prec : JLInt64) : Exports == Implementation where
+ExtendedNMPadicInteger(p : NMInteger, prec : JLInt64) : Exports == Implementation where
   --unBalanced? : Boolean
   I    ==> Integer
   NNI  ==> NonNegativeInteger
@@ -67,15 +66,30 @@ InnerNMPadicInteger(p : NMInteger, prec : JLInt64) : Exports == Implementation w
   JI64 ==> JLInt64
   Exports ==> Join(NMCommutativeRing, NMPadicIntegerCategory(p)) with
     "+" : (NINT, %) -> %
-    ++ a + x is the addition of a NemoInteger and a p-adic Integer.
+    ++ a + x is the addition of a Julia Nemo Integer
+    ++ and a p-adic Integer.
     "+" : (%, I) -> %
-    ++ x + a is the addition of a p-adic integer and an Integer.
+    ++ x + a is the addition of a p-adic integer
+    ++ and an Integer.
     "+" : (%, NINT) -> %
-    ++ x is the addition of a p-adic integer and a Nemo integer.
+    ++ x is the addition of a p-adic integer
+    ++ and a Julia Nemo integer.
     "+" : (I, %) -> %
     ++ a + x is the addition of an Integer and a p-adic integer.
     ++ For example:
     ++ \example{p := 1 + 2*7 + 4*7^2 + O(7,3)$NPADICZ(7)}
+    "+" : (%, NFINT) -> %
+    ++ x is the addition of a p-adic integer
+    ++ and a Julia Nemo Fraction integer.
+    "+" : (NFINT, %) -> %
+    ++ x is the addition of Julia Nemo Fraction integer
+    ++ and a p-adic integer
+    "*" : (%, NFINT) -> %
+    ++ x is the multiplication of a p-adic integer
+    ++ and a Julia Nemo Fraction integer.
+    "*" : (NFINT, %) -> %
+    ++ x is the multiplication of Julia Nemo Fraction integer
+    ++ and a p-adic integer
     "*" : (NINT, %) -> %
     ++ a * x is the multiplication of a NemoInteger and a p-adic integer.
     "*" : (I, %) -> %
@@ -109,8 +123,10 @@ InnerNMPadicInteger(p : NMInteger, prec : JLInt64) : Exports == Implementation w
     ++ padic(x) returns x as the p-adic completion of the NM Integer.
     jpadic : NMFraction NMInteger -> %
     ++ padic(x) returns x as the p-adic completion of the NM Integer.
-    O : (NMInteger, NMInteger) -> %
-    ++ 
+    O : (NMInteger, JLInt64) -> %
+    ++ 0() creates the default Big-oh from domain parameters.
+    O : () -> %
+    ++ 0() returns the default Big-oh from domain parameters.
     prime : () -> NMInteger
     ++
     precision : % -> Integer
@@ -132,12 +148,13 @@ InnerNMPadicInteger(p : NMInteger, prec : JLInt64) : Exports == Implementation w
     Rep := SExpression
 
     -- Set up the field
-    INPADICZP := concat(["INPADICZ", string(p), "p",string(prec)])
-    jlEvalString(concat([INPADICZP, "=padic_field(", getind(p), ", precision=", string(prec),")"]))
-    jlNMRing() == INPADICZP
-    INPADICZPP := concat(INPADICZP,"(")
-    jlObject() == jlEvalString(concat(["string(", INPADICZP,")"]))
-    O(p : NINT, e : NINT) == jlref(concat(["O(",INPADICZP,",", string(p),"^",string(e),")"]))
+    EXPADICZP := concat(["EXPADICZ", string(p), "p",string(prec)])
+    jlEvalString(concat([EXPADICZP, "=padic_field(", getind(p), ", precision=", string(prec),")"]))
+    jlNMRing() == EXPADICZP
+    EXPADICZPP := concat(EXPADICZP,"(")
+    jlObject() == jlEvalString(concat(["string(", EXPADICZP,")"]))
+    O(p, e) == jlref(concat(["O(",EXPADICZP,",", string(p),"^",string(e),")"]))
+    O() == jlref(concat(["O(",EXPADICZP,",", string(p),"^",string(prec),")"]))
 
     unit?(a) == junbfunc("is_unit", a)
     one?(a) == junbfunc("isone", a)
@@ -201,8 +218,8 @@ InnerNMPadicInteger(p : NMInteger, prec : JLInt64) : Exports == Implementation w
     --    st := rst st
     --  error "order: series has more than 1000 leading zero coefs"
 
-    0 ==  jlref(concat ["zero(", INPADICZP, ")"])
-    1 ==  jlref(concat ["one(", INPADICZP, ")"])
+    0 ==  jlref(concat ["zero(", EXPADICZP, ")"])
+    1 ==  jlref(concat ["one(", EXPADICZP, ")"])
     a : NINT + pa : % == jbinfunc("+",a,pa)
     a : Integer + pa : % == jbinfunc("+",jnint(a),pa)
     a : NINT * pa : % == jbinfunc("*",a,pa)
@@ -211,24 +228,28 @@ InnerNMPadicInteger(p : NMInteger, prec : JLInt64) : Exports == Implementation w
     pa : % + a : I == jbinfunc("+", pa, jnint a)
     pa : % * a : NINT == jbinfunc("*", pa, a)
     pa : % * a : I == jbinfunc("*", pa, jnint a)
-    coerce(i : Integer) == junfunc(INPADICZPP, string(i))
-    coerce(i : NMInteger) == junfunc(INPADICZP, i)
-    coerce(fi : NMFraction(NMInteger)) == junfunc(INPADICZP, fi)
-    jpadic(x) == jlref(concat([INPADICZPP, string(x),")"]))
-    jpadic(fi : NMFraction(NMInteger)) == junfunc(INPADICZP, fi)
+    pa : % * a : NFINT == jbinfunc("*", pa, a)
+    a  : NFINT * pa: % == jbinfunc("*", a, pa)
+    pa : % + a : NFINT == jbinfunc("+", pa, a)
+    a  : NFINT + pa: % == jbinfunc("+", a, pa)
+    coerce(i : Integer) == junfunc(EXPADICZPP, string(i))
+    coerce(i : NMInteger) == junfunc(EXPADICZP, i)
+    coerce(fi : NMFraction(NMInteger)) == junfunc(EXPADICZP, fi)
+    jpadic(x) == jlref(concat([EXPADICZPP, string(x),")"]))
+    jpadic(fi : NMFraction(NMInteger)) == junfunc(EXPADICZP, fi)
     coerce(x) : OUT == string(x) pretend OUT
 
 )abbrev domain NPADICZ NMPadicInteger
 ++ Author: Grégory Vanuxem
 ++ Date Created: 3 February 2025
 ++ Basic Operations:
-++ Related Domains: InnerNMPadicInteger
+++ Related Domains: ExtendedNMPadicInteger
 ++ Also See: NMPadicIntegerCategory
 ++ AMS Classifications:
 ++ Keywords: p-adic, completion
 ++ Examples:
 ++ References:
 ++ Description:
-++   Stream-based implementation of Zp: p-adic numbers are represented as
+++   Implementation of Zp: p-adic numbers are represented as
 ++   sum(i = 0.., a[i] * p^i), where the a[i] lie in 0, 1, ..., (p - 1).
-NMPadicInteger(p : NMInteger) == InnerNMPadicInteger(p, 30::JLInt64)
+NMPadicInteger(p : NMInteger) == ExtendedNMPadicInteger(p, 64::JLInt64)

src/algebra/jutils.spad

@@ -163,8 +163,10 @@ JLStringUtilities() : Exports == Implementation where
     ++ jlLatex(str) returns the String corresponding to a JL
     ++ LaTeX expression, that is, "styled_"str_"" if your JL support it.
     ++ (StyledStrings official package). Convenience function.
+    jlString : String -> String
+    ++ jlString(str) costructs an escaped string usable by the Julie parser.
     jlRegexMatch?   : (String, String) -> Boolean
-    ++ jlRegexMatch(s, regex) checks if the regular expression matches in s.
+    ++ jlRegexMatch?(s, regex) checks if the regular expression matches in s.
     jlRegexMatch    : (String, String) -> String
     ++ jlRegexMatch(s, regex) returns the matched regular expression in s.
     jlRegexMatch    : (String, String, PI) -> String
@@ -199,6 +201,7 @@ JLStringUtilities() : Exports == Implementation where
     jlMessageStyled(mess, color) ==
       jlEvalString(concat ["printstyled(" "_"\n     ", mess,
         "\n_";color=", string(color), ")"])
+    jlString(str) == concat(["_"", str, "_""])
     jlMessageStyled(mess) ==
       jl_eval_string(concat(["println(styled_"\n     ",mess,"_")"]))$Lisp
 
@@ -302,7 +305,7 @@ JLObjDynamicLinker() : Exports == Implementation where
     ++ Returned value is assumed to be a C type ctype
     ++ (or any JL supported types). For example:
     ++ \example{libm:= jlDlOpen "libopenlibm"}
-    ++ \example{squareRoot:= jlDlSym(libm,jsym(sqrt))}
+    ++ \example{squareRoot:= jlDlSym(libm,jsym(sqrt)}
     ++ \example{jlDlCApply(squareRoot, "Cdouble" jobject("2."), "Cdouble")}
     ++ \example{sinus:=jlDlSym(libm,jsym(sin))}
     ++ \example{jlDlCApply(sinus,"Float64"), jobject("2."), "Float64")}
@@ -327,7 +330,7 @@ JLObjDynamicLinker() : Exports == Implementation where
     ++ For example with GSL:
     ++ \example{gsl:= jlDlOpen "libgsl"}
     ++ \example{hypot3:= jlDlSym(gsl,jsym(gsl_hypot3))}
-    ++ \example{jlDlCApply(hypot3,jobject("2."),jobject("7."),jobjet("9.0"))}
+    ++ \example{jlDlCApply(hypot3,jobject("2."),jobject("7."),jobject("9.0"))}
     jlDlCApply : (%, STR, JOBJ, STR, JOBJ, STR, JOBJ, STR) -> JOBJ
     ++ jlDlCApply(func, ctype, x, xctype, y, xctype, z, ztype) applies the
     ++ function pointer func to x given its JL C type (xctype) or its