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Fix trailing white space
1 parent f436386 commit 03dac77

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Lines changed: 30 additions & 30 deletions

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‎src/Symbolics/Expression.fs‎

Lines changed: 30 additions & 30 deletions
Original file line numberDiff line numberDiff line change
@@ -121,7 +121,7 @@ module ExpressionPatterns =
121121
| Function (Sin, _) | Function (Cos, _) as r -> Some (r, Number BigRational.One)
122122
| Function (Sinh, _) | Function (Cosh, _) as r -> Some (r, Number BigRational.One)
123123
| Power (Function (Sin, _) as r, (Number n as p)) when n.IsInteger && n.IsPositive -> Some (r, p)
124-
| Power (Function (Cos, _) as r, (Number n as p)) when n.IsInteger && n.IsPositive -> Some (r, p)
124+
| Power (Function (Cos, _) as r, (Number n as p)) when n.IsInteger && n.IsPositive -> Some (r, p)
125125
| Power (Function (Sinh, _) as r, (Number n as p)) when n.IsInteger && n.IsPositive -> Some (r, p)
126126
| Power (Function (Cosh, _) as r, (Number n as p)) when n.IsInteger && n.IsPositive -> Some (r, p)
127127
| _ -> None
@@ -342,15 +342,15 @@ module Operators =
342342
| oo, Zero when isInfinity oo -> undefined
343343
| oo, PositiveInfinity when isInfinity oo -> complexInfinity
344344
| oo, Number b when isInfinity oo && b.IsNegative -> zero
345-
| ComplexInfinity, Positive -> complexInfinity
345+
| ComplexInfinity, Positive -> complexInfinity
346346
| PositiveInfinity, Positive -> infinity
347347
| NegativeInfinity, Number b when b.IsPositive && b.IsInteger ->
348348
if (b.Numerator % 2I).IsZero then infinity else negativeInfinity
349349
| One, oo | MinusOne, oo when isInfinity oo -> undefined
350350
| _, Zero | One, _ -> one
351351
| a, One -> a
352352
| Positive, PositiveInfinity -> infinity
353-
| Negative, PositiveInfinity -> complexInfinity
353+
| Negative, PositiveInfinity -> complexInfinity
354354
| _, NegativeInfinity -> zero
355355
| _, ComplexInfinity -> undefined
356356
| Number a, Number b when not (b.IsInteger) -> Power (x,y)
@@ -366,7 +366,7 @@ module Operators =
366366
let rec invert = function
367367
| Undefined -> undefined
368368
| Zero -> complexInfinity
369-
| oo when isInfinity oo -> zero
369+
| oo when isInfinity oo -> zero
370370
| Values.Value v -> Values.invert v
371371
| Product ax -> Product (ax |> List.map invert)
372372
| Power (r, p) -> pow r (negate p)
@@ -396,7 +396,7 @@ module Operators =
396396
| NegativeInfinity -> zero
397397
| Zero -> one
398398
| One -> Constant E
399-
| MinusOne -> invert (Constant E)
399+
| MinusOne -> invert (Constant E)
400400
| Product [Constant Pi; Constant I;] -> minusOne // exp(n*pi*j) for ...-1, -1/2, 0, 1/2, 1,...
401401
| Product [Number n; Constant Pi; Constant I;] when n.IsInteger
402402
-> if n.Numerator.IsEven then one else minusOne
@@ -468,7 +468,7 @@ module Operators =
468468
| Function (Acos, x') -> divide (sqrt (subtract one (pow x' two))) x' // tan(acos(x)) = sqrt(1 - x^2)/x
469469
| Function (Atan, x') -> x' // tan(atan(x)) = x
470470
| Function (Acsc, x') -> invert (multiply x' (sqrt (subtract one (invert (pow x' two))))) // tan(acsc(x)) = 1/(sqrt(1 - 1/x^2)*x)
471-
| Function (Asec, x') -> multiply x' (sqrt (subtract one (invert (pow x' two)))) // tan(asec(x)) = x*sqrt(1 - 1/x^2)
471+
| Function (Asec, x') -> multiply x' (sqrt (subtract one (invert (pow x' two)))) // tan(asec(x)) = x*sqrt(1 - 1/x^2)
472472
| Function (Acot, x') -> invert x' // tan(acot(x)) = 1/x
473473
| x -> Function (Tan, x)
474474
let csc = function
@@ -478,7 +478,7 @@ module Operators =
478478
| Constant Pi -> complexInfinity // csc(pi) = coo
479479
| Constant I -> Function (Csch, one) |> multiply (Constant I) |> negate // csc(j) = -j*csch(1), csc(j*x) = -j*csch(x)
480480
| Number n when n.IsNegative -> Function (Csc, Number -n) |> negate // csc(-x) = -csc(x)
481-
| Product ((Number n)::ax) when n.IsNegative -> Function (Csc, multiply (Number -n) (Product ax)) |> negate
481+
| Product ((Number n)::ax) when n.IsNegative -> Function (Csc, multiply (Number -n) (Product ax)) |> negate
482482
| Function (Asin, x') -> invert x' // csc(asin(x)) = 1/x
483483
| Function (Acos, x') -> invert (sqrt (subtract one (pow x' two))) // csc(acos(x)) = 1/sqrt(1 - x^2)
484484
| Function (Atan, x') -> divide (sqrt (add one (pow x' two))) x' // csc(atan(x)) = sqrt(1 + x^2)/x
@@ -493,7 +493,7 @@ module Operators =
493493
| Constant Pi -> minusOne // sec(pi) = -1
494494
| Constant I -> Function (Sech, one) // sec(j) = sech(1), sec(j*x) = sech(x)
495495
| Number n when n.IsNegative -> Function (Sec, Number -n) // sec(-x) = sec(x)
496-
| Product ((Number n)::ax) when n.IsNegative -> Function (Sec, multiply (Number -n) (Product ax))
496+
| Product ((Number n)::ax) when n.IsNegative -> Function (Sec, multiply (Number -n) (Product ax))
497497
| Function (Asin, x') -> invert (sqrt (subtract one (pow x' two))) // sec(asin(x)) = 1/sqrt(1 - x^2)
498498
| Function (Acos, x') -> invert x' // sec(acos(x)) = 1/x
499499
| Function (Atan, x') -> sqrt (add one (pow x' two)) // sec(atan(x)) = sqrt(1 + x^2)
@@ -505,14 +505,14 @@ module Operators =
505505
| Undefined -> undefined
506506
| oo when isInfinity oo -> undefined
507507
| Zero -> complexInfinity // cot(0) = coo
508-
| Constant Pi -> complexInfinity // cot(pi) = coo
508+
| Constant Pi -> complexInfinity // cot(pi) = coo
509509
| Constant I -> Function (Coth, one) |> multiply (Constant I) |> negate // cot(j) = -j*coth(1), cot(j*x) = -j*coth(x)
510510
| Number n when n.IsNegative -> Function (Cot, Number -n) |> negate // cot(-x) = -cot(x)
511-
| Product ((Number n)::ax) when n.IsNegative -> Function (Cot, multiply (Number -n) (Product ax)) |> negate
511+
| Product ((Number n)::ax) when n.IsNegative -> Function (Cot, multiply (Number -n) (Product ax)) |> negate
512512
| Function (Asin, x') -> divide (sqrt (subtract one (pow x' two))) x' // cot(asin(x)) = sqrt(1 - x^2)/x
513513
| Function (Acos, x') -> divide x' (sqrt (subtract one (pow x' two))) // cot(acos(x)) = x/sqrt(1 - x^2)
514514
| Function (Atan, x') -> invert x' // cot(atan(x)) = 1/x
515-
| Function (Acsc, x') -> multiply x' (sqrt (subtract one (invert (pow x' two)))) // cot(acsc(x)) = x*sqrt(1 - 1/x^2)
515+
| Function (Acsc, x') -> multiply x' (sqrt (subtract one (invert (pow x' two)))) // cot(acsc(x)) = x*sqrt(1 - 1/x^2)
516516
| Function (Asec, x') -> invert (multiply x' (sqrt (subtract one (invert (pow x' two))))) // cot(asec(x)) = 1/(x*sqrt(1 - 1/x^2))
517517
| Function (Acot, x') -> x' // cot(acot(x)) = x
518518
| x -> Function (Cot, x)
@@ -524,7 +524,7 @@ module Operators =
524524
| Zero -> zero // sinh(0) = 0
525525
| Constant I -> Function (Sin, one) |> multiply (Constant I) // sinh(j) = j*sin(1), sinh(j*x) = j*sin(x)
526526
| Number n when n.IsNegative -> Function (Sinh, Number -n) |> negate // sinh(-x) = -sinh(x)
527-
| Product ((Number n)::ax) when n.IsNegative -> Function (Sinh, multiply (Number -n) (Product ax)) |> negate
527+
| Product ((Number n)::ax) when n.IsNegative -> Function (Sinh, multiply (Number -n) (Product ax)) |> negate
528528
| Function (Asinh, x') -> x' // sinh(asinh(x)) = x
529529
| Function (Acosh, x') -> multiply (add one x') (sqrt (divide (subtract x' one) (add x' one))) // sinh(acosh(x)) = (x + 1)*sqrt((x - 1)/(x + 1))
530530
| Function (Atanh, x') -> divide x' (sqrt (subtract one (pow x' two))) // sinh(atanh(x)) = x/sqrt(1 - x^2)
@@ -535,30 +535,30 @@ module Operators =
535535
let cosh = function
536536
| Undefined | ComplexInfinity -> undefined
537537
| PositiveInfinity | NegativeInfinity -> infinity // cosh(oo) = cosh(-oo) = oo
538-
| Zero -> one // cosh(0) = 1
538+
| Zero -> one // cosh(0) = 1
539539
| Constant I -> Function (Cos, one) // cosh(j) = cos(1), cosh(j*x) = cos(x)
540540
| Number n when n.IsNegative -> Function (Cosh, Number -n) // cosh(-x) = cosh(x)
541-
| Product ((Number n)::ax) when n.IsNegative -> Function (Cosh, multiply (Number -n) (Product ax))
541+
| Product ((Number n)::ax) when n.IsNegative -> Function (Cosh, multiply (Number -n) (Product ax))
542542
| Function (Asinh, x') -> sqrt (add (pow x' two) one) // cosh(asinh(x)) = sqrt(x^2 + 1)
543543
| Function (Acosh, x') -> x' // cosh(acosh(x)) = x
544544
| Function (Atanh, x') -> invert (sqrt (subtract one (pow x' two))) // cosh(atanh(x)) = 1/sqrt(1 - x^2)
545545
| Function (Acsch, x') -> sqrt (add (invert (pow x' two)) one) // cosh(acsch(x)) = sqrt(1/x^2 + 1)
546546
| Function (Asech, x') -> invert x' // cosh(asech(x)) = 1/x
547547
| Function (Acoth, x') -> invert (sqrt (subtract one (invert (pow x' two)))) // cosh(acoth(x)) = 1/sqrt(1 - 1/x^2)
548-
| x -> Function (Cosh, x)
548+
| x -> Function (Cosh, x)
549549
let tanh = function
550550
| Undefined | ComplexInfinity -> undefined
551551
| PositiveInfinity -> one // tanh(oo) = 1, tanh(-oo) = -1
552552
| NegativeInfinity -> minusOne
553553
| Zero -> zero // tanh(0) = 0
554554
| Constant I -> Function (Tan, one) |> multiply (Constant I) // tanh(j) = j*tan(1), tanh(j*x) = j*tan(x)
555555
| Number n when n.IsNegative -> Function (Tanh, Number -n) |> negate // tanh(-x) = -tanh(x)
556-
| Product ((Number n)::ax) when n.IsNegative -> Function (Tanh, multiply (Number -n) (Product ax)) |> negate
556+
| Product ((Number n)::ax) when n.IsNegative -> Function (Tanh, multiply (Number -n) (Product ax)) |> negate
557557
| Function (Asinh, x') -> divide x' (sqrt (add (pow x' two) one)) // tanh(asinh(x)) = x/sqrt(x^2 + 1)
558558
| Function (Acosh, x') -> divide (multiply (add x' one) (sqrt (divide (subtract x' one) (add x' one)))) x' // tanh(acosh(x)) = ((x + 1)*sqrt((x - 1)/(x + 1)))/x
559559
| Function (Atanh, x') -> x' // tanh(atanh(x)) = x
560560
| Function (Acsch, x') -> invert (multiply x' (sqrt (add (invert (pow x' two)) one))) // tanh(acsch(x)) = 1/(x*sqrt(1/x^2 + 1))
561-
| Function (Asech, x') -> multiply (add x' one) (sqrt(divide (subtract one x') (add x' one))) // tanh(asech(x)) = (x + 1)*sqrt((1 - x)/(x + 1))
561+
| Function (Asech, x') -> multiply (add x' one) (sqrt(divide (subtract one x') (add x' one))) // tanh(asech(x)) = (x + 1)*sqrt((1 - x)/(x + 1))
562562
| Function (Acoth, x') -> invert x' // tanh(acoth(x)) = 1/x
563563
| x -> Function (Tanh, x)
564564
let csch = function
@@ -567,7 +567,7 @@ module Operators =
567567
| Zero -> complexInfinity // csch(0) = coo
568568
| Constant I -> Function (Csc, one) |> multiply (Constant I) |> negate // csch(j) = -j*csc(1), csch(j*x) = -j*csc(x)
569569
| Number n when n.IsNegative -> Function (Csch, Number -n) |> negate // csch(-x) = -csch(x)
570-
| Product ((Number n)::ax) when n.IsNegative -> Function (Csch, multiply (Number -n) (Product ax)) |> negate
570+
| Product ((Number n)::ax) when n.IsNegative -> Function (Csch, multiply (Number -n) (Product ax)) |> negate
571571
| Function (Asinh, x') -> invert x' // csch(asinh(x)) = 1/x
572572
| Function (Acosh, x') -> invert (multiply (add one x') (sqrt (divide (subtract x' one) (add x' one)))) // csch(acosh(x)) = 1/((x + 1)*sqrt((x - 1)/(x + 1)))
573573
| Function (Atanh, x') -> divide (sqrt (subtract one (pow x' two))) x' // csch(atanh(x)) = sqrt(1 - x^2)/x
@@ -581,7 +581,7 @@ module Operators =
581581
| Zero -> one // sech(0) = 1
582582
| Constant I -> Function (Sec, one) // sech(j*x) = sec(x)
583583
| Number n when n.IsNegative -> Function (Sech, Number -n) // sech(-x) = sech(x)
584-
| Product ((Number n)::ax) when n.IsNegative -> Function (Sech, multiply (Number -n) (Product ax))
584+
| Product ((Number n)::ax) when n.IsNegative -> Function (Sech, multiply (Number -n) (Product ax))
585585
| Function (Asinh, x') -> invert (sqrt (add (pow x' two) one)) // sech(asinh(x)) = 1/sqrt(x^2 + 1)
586586
| Function (Acosh, x') -> invert x' // sech(acosh(x)) = 1/x
587587
| Function (Atanh, x') -> sqrt (subtract one (pow x' two)) // sech(atanh(x)) = sqrt(1 - x^2)
@@ -595,7 +595,7 @@ module Operators =
595595
| Zero -> complexInfinity
596596
| Constant I -> Function (Cot, one) |> multiply (Constant I) |> negate // coth(j*x) = -j*cot(x)
597597
| Number n when n.IsNegative -> Function (Coth, Number -n) |> negate // coth(-x) = -coth(x)
598-
| Product ((Number n)::ax) when n.IsNegative -> Function (Coth, multiply (Number -n) (Product ax)) |> negate
598+
| Product ((Number n)::ax) when n.IsNegative -> Function (Coth, multiply (Number -n) (Product ax)) |> negate
599599
| Function (Asinh, x') -> divide (sqrt (add (pow x' two) one)) x' // coth(asinh(x)) = sqrt(x^2 + 1)/x
600600
| Function (Acosh, x') -> divide x' (multiply (add x' one) (sqrt (divide (subtract x' one) (add x' one)))) // coth(acosh(x)) = x/((x + 1)*sqrt((x - 1)/(x + 1)))
601601
| Function (Atanh, x') -> invert x' // coth(atanh(x)) = 1/x
@@ -652,7 +652,7 @@ module Operators =
652652
| oo when isInfinity oo -> zero // acot(coo) = acot(oo) = acot(-oo) = 0
653653
| Zero -> divide pi two // acot(0) = pi/2
654654
| One -> divide pi four // acot(1) = pi/4, acot(-1) = -pi/4
655-
| MinusOne -> divide pi four |> negate
655+
| MinusOne -> divide pi four |> negate
656656
| Constant I -> multiply (Constant I) negativeInfinity // atan(j) = -oo*j
657657
| Number n when n.IsNegative -> Function (Acot, Number -n) |> negate // acot(-x) = -acot(x)
658658
| Product ((Number n)::ax) when n.IsNegative -> Function (Acot, multiply (Number -n) (Product ax)) |> negate
@@ -662,10 +662,10 @@ module Operators =
662662
| Undefined | ComplexInfinity -> undefined
663663
| PositiveInfinity -> infinity // asinh(oo) = oo, asinh(-oo) = -oo
664664
| NegativeInfinity -> negativeInfinity
665-
| Zero -> zero // asinh(0) = 0
665+
| Zero -> zero // asinh(0) = 0
666666
| Constant I -> divide (multiply pi (Constant I)) two // asinh(j) = pi*j/2, asinh(n*j) = j*asin(n)
667667
| Number n when n.IsNegative -> Function (Asinh, Number -n) |> negate // asinh(-x) = -asinh(x)
668-
| Product ((Number n)::ax) when n.IsNegative -> Function (Asinh, multiply (Number -n) (Product ax)) |> negate
668+
| Product ((Number n)::ax) when n.IsNegative -> Function (Asinh, multiply (Number -n) (Product ax)) |> negate
669669
| x -> Function (Asinh, x)
670670
let arccosh = function
671671
| Undefined | ComplexInfinity -> undefined
@@ -683,15 +683,15 @@ module Operators =
683683
| MinusOne -> negativeInfinity
684684
| Constant I -> divide (multiply pi (Constant I)) four // atanh(j) = pi*j/4
685685
| Number n when n.IsNegative -> Function (Atanh, Number -n) |> negate // atanh(-x) = -atanh(x)
686-
| Product ((Number n)::ax) when n.IsNegative -> Function (Atanh, multiply (Number -n) (Product ax)) |> negate
686+
| Product ((Number n)::ax) when n.IsNegative -> Function (Atanh, multiply (Number -n) (Product ax)) |> negate
687687
| x -> Function (Atanh, x)
688688
let arccsch = function
689689
| Undefined | ComplexInfinity -> undefined
690690
| PositiveInfinity | NegativeInfinity -> zero // acsch(oo) = acsch(-oo) = 0
691-
| Zero | One | MinusOne -> complexInfinity // acsch(0) = coo
691+
| Zero | One | MinusOne -> complexInfinity // acsch(0) = coo
692692
| Constant I -> divide (multiply pi (Constant I)) two |> negate // acsch(j) = -pi*j/2
693693
| Number n when n.IsNegative -> Function (Acsch, Number -n) |> negate // acsch(-x) = -acsch(x)
694-
| Product ((Number n)::ax) when n.IsNegative -> Function (Acsch, multiply (Number -n) (Product ax)) |> negate
694+
| Product ((Number n)::ax) when n.IsNegative -> Function (Acsch, multiply (Number -n) (Product ax)) |> negate
695695
| x -> Function (Acsch, x)
696696
let arcsech = function
697697
| Undefined | ComplexInfinity -> undefined
@@ -708,7 +708,7 @@ module Operators =
708708
| MinusOne -> negativeInfinity
709709
| Constant I -> divide (multiply pi (Constant I)) four |> negate // atanh(j) = -pi*j/4
710710
| Number n when n.IsNegative -> Function (Acoth, Number -n) |> negate // acoth(-x) = -acoth(x)
711-
| Product ((Number n)::ax) when n.IsNegative -> Function (Acoth, multiply (Number -n) (Product ax)) |> negate
711+
| Product ((Number n)::ax) when n.IsNegative -> Function (Acoth, multiply (Number -n) (Product ax)) |> negate
712712
| x -> Function (Acoth, x)
713713

714714
let apply f x =
@@ -728,7 +728,7 @@ module Operators =
728728
| Tanh -> tanh x
729729
| Csch -> csch x
730730
| Sech -> sech x
731-
| Coth -> coth x
731+
| Coth -> coth x
732732
| Asin -> arcsin x
733733
| Acos -> arccos x
734734
| Atan -> arctan x
@@ -741,7 +741,7 @@ module Operators =
741741
| Acsch -> arccsch x
742742
| Asech -> arcsech x
743743
| Acoth -> arccoth x
744-
744+
745745

746746
let applyN (f: Function) (xs: Expression list) =
747747
match f, xs with
@@ -796,7 +796,7 @@ type Expression with
796796
static member Cot (x) = Operators.cot x
797797

798798
static member Sinh (x) = Operators.sinh x
799-
static member Cosh (x) = Operators.cosh x
799+
static member Cosh (x) = Operators.cosh x
800800
static member Tanh (x) = Operators.tanh x
801801
static member Coth (x) = Operators.coth x
802802
static member Csch (x) = Operators.csch x

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