v0.5.4.0

stla · Jun 19, 2024 · 671d0a2 · 671d0a2
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diff --git a/CHANGELOG.md b/CHANGELOG.md
@@ -306,7 +306,11 @@ interval. This can be very slow if the degree of the spray is not small.
 polynomial whose leading coefficient is 1.
 
 
-## 0.5.4.0 - 2024-06-XX
+## 0.5.4.0 - 2024-06-19
 
 * Now the greatest common divisor of two sprays (function `gcdSpray`) is 
 always monic, i.e. it is a polynomial whose leading coefficient is 1.
+
+* Function `evalRatioOfSprays'`, to substitute the variables of a ratio of
+sprays with some ratios of sprays.
+
diff --git a/src/Math/Algebra/Hspray.hs b/src/Math/Algebra/Hspray.hs
@@ -3019,19 +3019,6 @@ pseudoDivision' n sprayA sprayB
         q            = ellB ^**^ e
         sprayS       = multSprayByTerm ellR (loneTerm' n (degR - degB))
 
-{- spray1,spray2 :: QSpray
-spray1 = let x = qlone 1
-             y = qlone 2
-             z = qlone 3
-         in
-          (-5)*^x^**^3 ^-^ 11*^(x^**^2^*^y) ^-^ 11*^(x^*^y^**^2) ^-^ 8*^(x^*^y^*^z) ^+^ 20*^(x^*^z^**^2) ^-^ 5*^y^**^3 ^+^ 20*^(y^*^z^**^2)
-spray2 = let x = qlone 1
-             y = qlone 2
-             z = qlone 3
-         in
-          x^*^y ^-^ x^*^z ^-^ y^*^z ^+^ z^**^2
- -}
-
 -- | recursive GCD function
 gcdKX1dotsXn :: forall a. (Eq a, AlgField.C a) 
                 => Int -> Spray a -> Spray a -> Spray a
@@ -3088,73 +3075,6 @@ gcdSpray sprayA sprayB = gcdKX1dotsXn n sprayA sprayB
   where
     n = max (numberOfVariables sprayA) (numberOfVariables sprayB)
 
--- test :: QSpray
--- test = gcdSpray sprayA sprayB
---   where
---      sprayA = HM.fromList [(Powers {exponents = S.fromList [1,4], nvariables = 2},2),(Powers {exponents = S.fromList [3,4], nvariables = 2},-1),(Powers {exponents = S.fromList [4,2], nvariables = 2},1),(Powers {exponents = S.fromList [2,4], nvariables = 2},2),(Powers {exponents = S.fromList [3,2], nvariables = 2},1),(Powers {exponents = S.fromList [1], nvariables = 1},1),(Powers {exponents = S.fromList [], nvariables = 0},-2),(Powers {exponents = S.fromList [2,2], nvariables = 2},1),(Powers {exponents = S.fromList [4,4], nvariables = 2},-3),(Powers {exponents = S.fromList [1,2], nvariables = 2},-3),(Powers {exponents = S.fromList [2,5], nvariables = 2},-1),(Powers {exponents = S.fromList [3,5], nvariables = 2},-1),(Powers {exponents = S.fromList [0,1], nvariables = 2},3),(Powers {exponents = S.fromList [2,3], nvariables = 2},-1),(Powers {exponents = S.fromList [4,5], nvariables = 2},2),(Powers {exponents = S.fromList [1,1], nvariables = 2},1),(Powers {exponents = S.fromList [3,3], nvariables = 2},3),(Powers {exponents = S.fromList [0,3], nvariables = 2},-1),(Powers {exponents = S.fromList [2,1], nvariables = 2},-2),(Powers {exponents = S.fromList [1,3], nvariables = 2},-1),(Powers {exponents = S.fromList [2], nvariables = 1},1),(Powers {exponents = S.fromList [3,1], nvariables = 2},-2)]
---      sprayB = HM.fromList [(Powers {exponents = S.fromList [5,2], nvariables = 2},-2),(Powers {exponents = S.fromList [4,2], nvariables = 2},3),(Powers {exponents = S.fromList [1], nvariables = 1},2),(Powers {exponents = S.fromList [], nvariables = 0},-1),(Powers {exponents = S.fromList [2,2], nvariables = 2},-1),(Powers {exponents = S.fromList [4,1], nvariables = 2},1),(Powers {exponents = S.fromList [6,3], nvariables = 2},1),(Powers {exponents = S.fromList [4,3], nvariables = 2},1),(Powers {exponents = S.fromList [5,3], nvariables = 2},-2),(Powers {exponents = S.fromList [1,1], nvariables = 2},2),(Powers {exponents = S.fromList [2,1], nvariables = 2},-3),(Powers {exponents = S.fromList [2], nvariables = 1},-1)]
---      -- x = qlone 1
---      -- y = qlone 2
---      -- sprayA = 2*^(x^**^4^*^y^**^5) ^-^ 3*^(x^**^4^*^y^**^4) ^+^ x^**^4^*^y^**^2 ^-^ x^**^3^*^y^**^5 ^-^ x^**^3^*^y^**^4 ^+^ 3*^(x^**^3^*^y^**^3) ^+^ x^**^3^*^y^**^2 ^-^ 2*^(x^**^3^*^y) ^-^ x^**^2^*^y^**^5 ^+^ 2*^(x^**^2^*^y^**^4) ^-^ x^**^2^*^y^**^3 ^+^ x^**^2^*^y^**^2 ^-^ 2*^(x^**^2^*^y) ^+^ x^**^2 ^+^ 2*^(x^*^y^**^4) ^-^ x^*^y^**^3 ^-^ 3*^(x^*^y^**^2) ^+^ x^*^y ^+^ x ^-^ y^**^3 ^+^ 3*^y ^-^ 2*^unitSpray
---      -- sprayB = x^**^6^*^y^**^3 ^-^ 2*^(x^**^5^*^y^**^3) ^-^ 2*^(x^**^5^*^y^**^2) ^+^ x^**^4^*^y^**^3 ^+^ 3*^(x^**^4^*^y^**^2) ^+^ x^**^4^*^y ^-^ x^**^2^*^y^**^2 ^-^ 3*^(x^**^2^*^y) ^-^ x^**^2 ^+^ 2*^(x^*^y) ^+^ 2*^x ^-^ unitSpray
-
--- test :: (QSpray,QSpray)
--- test = (sprayA, sprayB)
---   where
---      fromList = S.fromList
---      (%) = (DR.%)
---      sprayA = HM.fromList [(Powers {exponents = fromList [1,4], nvariables = 2},13 % 1),(Powers {exponents = fromList [9,12], nvariables = 2},1 % 1),(Powers {exponents = fromList [3,6], nvariables = 2},(-24) % 1),(Powers {exponents = fromList [2,6], nvariables = 2},(-12) % 1),(Powers {exponents = fromList [6,2], nvariables = 2},(-4) % 1),(Powers {exponents = fromList [1,6], nvariables = 2},(-4) % 1),(Powers {exponents = fromList [3,4], nvariables = 2},42 % 1),(Powers {exponents = fromList [11,12], nvariables = 2},2 % 1),(Powers {exponents = fromList [5,2], nvariables = 2},(-12) % 1),(Powers {exponents = fromList [4,2], nvariables = 2},(-16) % 1),(Powers {exponents = fromList [2,4], nvariables = 2},31 % 1),(Powers {exponents = fromList [10,12], nvariables = 2},3 % 1),(Powers {exponents = fromList [9,8], nvariables = 2},(-31) % 1),(Powers {exponents = fromList [3,2], nvariables = 2},(-18) % 1),(Powers {exponents = fromList [11,10], nvariables = 2},(-2) % 1),(Powers {exponents = fromList [5,4], nvariables = 2},26 % 1),(Powers {exponents = fromList [7,6], nvariables = 2},28 % 1),(Powers {exponents = fromList [1], nvariables = 1},(-3) % 1),(Powers {exponents = fromList [6,6], nvariables = 2},12 % 1),(Powers {exponents = fromList [], nvariables = 0},(-2) % 1),(Powers {exponents = fromList [8,8], nvariables = 2},(-42) % 1),(Powers {exponents = fromList [2,2], nvariables = 2},(-18) % 1),(Powers {exponents = fromList [10,10], nvariables = 2},6 % 1),(Powers {exponents = fromList [4,4], nvariables = 2},44 % 1),(Powers {exponents = fromList [5,6], nvariables = 2},(-12) % 1),(Powers {exponents = fromList [1,2], nvariables = 2},(-6) % 1),(Powers {exponents = fromList [9,10], nvariables = 2},18 % 1),(Powers {exponents = fromList [0,2], nvariables = 2},2 % 1),(Powers {exponents = fromList [8,10], nvariables = 2},18 % 1),(Powers {exponents = fromList [10,8], nvariables = 2},(-13) % 1),(Powers {exponents = fromList [4,6], nvariables = 2},(-28) % 1),(Powers {exponents = fromList [6,4], nvariables = 2},6 % 1),(Powers {exponents = fromList [7,10], nvariables = 2},16 % 1),(Powers {exponents = fromList [5,8], nvariables = 2},(-6) % 1),(Powers {exponents = fromList [10,6], nvariables = 2},4 % 1),(Powers {exponents = fromList [6,10], nvariables = 2},12 % 1),(Powers {exponents = fromList [9,6], nvariables = 2},12 % 1),(Powers {exponents = fromList [5,10], nvariables = 2},4 % 1),(Powers {exponents = fromList [7,8], nvariables = 2},(-44) % 1),(Powers {exponents = fromList [6,8], nvariables = 2},(-26) % 1),(Powers {exponents = fromList [8,6], nvariables = 2},24 % 1),(Powers {exponents = fromList [4,1], nvariables = 2},3 % 1),(Powers {exponents = fromList [6,3], nvariables = 2},15 % 1),(Powers {exponents = fromList [0,5], nvariables = 2},1 % 1),(Powers {exponents = fromList [2,7], nvariables = 2},5 % 1),(Powers {exponents = fromList [7,3], nvariables = 2},5 % 1),(Powers {exponents = fromList [1,5], nvariables = 2},3 % 1),(Powers {exponents = fromList [3,7], nvariables = 2},15 % 1),(Powers {exponents = fromList [5,1], nvariables = 2},1 % 1),(Powers {exponents = fromList [2,5], nvariables = 2},(-6) % 1),(Powers {exponents = fromList [4,3], nvariables = 2},6 % 1),(Powers {exponents = fromList [3,5], nvariables = 2},(-18) % 1),(Powers {exponents = fromList [5,3], nvariables = 2},18 % 1),(Powers {exponents = fromList [0,1], nvariables = 2},3 % 1),(Powers {exponents = fromList [8,9], nvariables = 2},3 % 1),(Powers {exponents = fromList [2,3], nvariables = 2},(-11) % 1),(Powers {exponents = fromList [10,11], nvariables = 2},(-11) % 1),(Powers {exponents = fromList [4,5], nvariables = 2},(-38) % 1),(Powers {exponents = fromList [6,7], nvariables = 2},54 % 1),(Powers {exponents = fromList [1,1], nvariables = 2},11 % 1),(Powers {exponents = fromList [9,9], nvariables = 2},11 % 1),(Powers {exponents = fromList [3,3], nvariables = 2},(-3) % 1),(Powers {exponents = fromList [11,11], nvariables = 2},(-3) % 1),(Powers {exponents = fromList [5,5], nvariables = 2},(-54) % 1),(Powers {exponents = fromList [7,7], nvariables = 2},38 % 1),(Powers {exponents = fromList [0,3], nvariables = 2},(-4) % 1),(Powers {exponents = fromList [8,11], nvariables = 2},(-6) % 1),(Powers {exponents = fromList [2,1], nvariables = 2},12 % 1),(Powers {exponents = fromList [10,9], nvariables = 2},14 % 1),(Powers {exponents = fromList [4,7], nvariables = 2},34 % 1),(Powers {exponents = fromList [6,5], nvariables = 2},(-50) % 1),(Powers {exponents = fromList [11,9], nvariables = 2},4 % 1),(Powers {exponents = fromList [5,7], nvariables = 2},50 % 1),(Powers {exponents = fromList [7,5], nvariables = 2},(-34) % 1),(Powers {exponents = fromList [1,3], nvariables = 2},(-14) % 1),(Powers {exponents = fromList [2], nvariables = 1},(-1) % 1),(Powers {exponents = fromList [9,11], nvariables = 2},(-12) % 1),(Powers {exponents = fromList [3,1], nvariables = 2},6 % 1),(Powers {exponents = fromList [10,7], nvariables = 2},(-3) % 1),(Powers {exponents = fromList [4,9], nvariables = 2},(-5) % 1),(Powers {exponents = fromList [6,11], nvariables = 2},(-1) % 1),(Powers {exponents = fromList [8,5], nvariables = 2},(-15) % 1),(Powers {exponents = fromList [5,9], nvariables = 2},(-15) % 1),(Powers {exponents = fromList [7,11], nvariables = 2},(-3) % 1),(Powers {exponents = fromList [9,5], nvariables = 2},(-5) % 1),(Powers {exponents = fromList [11,7], nvariables = 2},(-1) % 1),(Powers {exponents = fromList [6,9], nvariables = 2},(-18) % 1),(Powers {exponents = fromList [8,7], nvariables = 2},18 % 1),(Powers {exponents = fromList [9,7], nvariables = 2},6 % 1),(Powers {exponents = fromList [7,9], nvariables = 2},(-6) % 1)]
---      sprayB = HM.fromList [(Powers {exponents = fromList [3,4], nvariables = 2},13 % 1),(Powers {exponents = fromList [11,12], nvariables = 2},1 % 1),(Powers {exponents = fromList [6,6], nvariables = 2},14 % 1),(Powers {exponents = fromList [], nvariables = 0},(-1) % 1),(Powers {exponents = fromList [8,8], nvariables = 2},(-13) % 1),(Powers {exponents = fromList [2,2], nvariables = 2},(-13) % 1),(Powers {exponents = fromList [10,10], nvariables = 2},(-1) % 1),(Powers {exponents = fromList [4,4], nvariables = 2},14 % 1),(Powers {exponents = fromList [5,6], nvariables = 2},(-14) % 1),(Powers {exponents = fromList [1,2], nvariables = 2},1 % 1),(Powers {exponents = fromList [9,10], nvariables = 2},13 % 1),(Powers {exponents = fromList [7,8], nvariables = 2},(-14) % 1),(Powers {exponents = fromList [8,9], nvariables = 2},(-8) % 1),(Powers {exponents = fromList [2,3], nvariables = 2},(-6) % 1),(Powers {exponents = fromList [10,11], nvariables = 2},(-6) % 1),(Powers {exponents = fromList [4,5], nvariables = 2},(-8) % 1),(Powers {exponents = fromList [6,7], nvariables = 2},28 % 1),(Powers {exponents = fromList [1,1], nvariables = 2},6 % 1),(Powers {exponents = fromList [9,9], nvariables = 2},6 % 1),(Powers {exponents = fromList [3,3], nvariables = 2},8 % 1),(Powers {exponents = fromList [5,5], nvariables = 2},(-28) % 1),(Powers {exponents = fromList [7,7], nvariables = 2},8 % 1)]
-
--- gogo :: (QSpray, QSpray, QSpray, QSpray, QSpray) -> (QSpray, QSpray, QSpray, QSpray, QSpray)
--- gogo (sprayA'', sprayB'', g, h, _) =
---                (
---                     sprayB'' 
---                ,    (exactDivisionBy (g ^*^ h^**^delta) sprayR)
---                ,    ellB'' ---- ellA''
---                ,    (exactDivisionBy (h^**^delta) (h ^*^ ellB''^**^delta)) 
---                ,    sprayR
---                )
---    where
---      (_, (_, sprayR)) = pseudoDivision' 2 sprayA'' sprayB''
---      degA''           = degree 2 sprayA''
---      (degB'', ellB'') = degreeAndLeadingCoefficient 2 sprayB''
---      delta            = degA'' - degB''
---      exactDivisionBy b a = 
---       if isZeroSpray remainder 
---         then quo 
---         else error "exactDivisionBy: should not happen."
---       where
---         (quo, remainder) = sprayDivision a b
-
--- gogogo :: QSpray -> QSpray -> QSpray -> QSpray -> QSpray
--- gogogo sprayA'' sprayB'' g h 
---  | isZeroSpray sprayR            = sprayB''
---  | numberOfVariables sprayR == 0 = zeroSpray
---  | otherwise = gogogo sprayB'' 
---                   (exactDivisionBy (g ^*^ h^**^delta) sprayR)
---                   ellB'' ---- ellA''
---                   (exactDivisionBy (h^**^delta) (h ^*^ ellB''^**^delta)) --- g^**^delta
---    where
---      (_, (_, sprayR)) = pseudoDivision' 2 sprayA'' sprayB''
---      degA''           = degree 2 sprayA''
---      (degB'', ellB'') = degreeAndLeadingCoefficient 2 sprayB''
---      delta            = degA'' - degB''
---      exactDivisionBy b a = 
---       if isZeroSpray remainder 
---         then quo 
---         else error "exactDivisionBy: should not happen."
---       where
---         (quo, remainder) = sprayDivision a b
-
--- test' :: Int -> QSpray
--- test' n = q1 
---   where
---      (q1, _, _, _, _) = last $ take n $ iterate gogo (sprayA', sprayB, unitSpray , unitSpray , zeroSpray )
---      (sprayA, sprayB) = test
---      contA= foldl1' (gcdKX1dotsXn 1) (sprayCoefficients' 2 sprayA)
--- --     contA' = let leadingCoeff = snd $ leadingTerm contA in contA /> leadingCoeff
---      (sprayA',rrr) = sprayDivision sprayA contA
 
 -- Matrices -------------------------------------------------------------------
 
@@ -3443,7 +3363,10 @@ evalRatioOfSprays' (RatioOfSprays spray1 spray2) listOfROS =
         foldl' 
           (AlgRing.*) 
             unitRatioOfSprays 
-              (S.zipWith (\ros e -> ros AlgRing.^ (fromIntegral e)) seqOfROS (exponents powers))
+              (S.zipWith 
+                (\ros e -> 
+                  ros AlgRing.^ (fromIntegral e)) seqOfROS (exponents powers)
+              )
     eval_spray spray = 
       HM.foldl' 
         (AlgAdd.+)