finxed typos

Author: Bumblebee00

README.md

@@ -67,7 +67,7 @@ integrate(f, x, rbm)
 ```
 where:
 - `verbsoe` specifies whether to print or not the integration rules applied (default true)
-- `use_gamma` sepcifies whether to use rules with the gamma function in the result, or not (default false)
+- `use_gamma` specifies whether to use rules with the gamma function in the result, or not (default false)
 
 If no method is specified, first RischMethod will be tried, then RuleBasedMethod:
 ```julia

src/methods/risch/frontend.jl

@@ -16,15 +16,15 @@ of `D`, `D` is `d/dx` on `C(x)`, and `D` is iteratively extended from `C(x)(t₁
 such that `tᵢ` is monomial over `C(x)(t₁)...(tᵢ₋₁)` with `D(tᵢ)=Hᵢ=Hᵢ(x, t₁,....,tᵢ)`.
 The generators `x` of C(x) over C and `tᵢ` of `C(x)(t₁)...(tᵢ)` over `C(x)(t₁)...(tᵢ₋₁)` are returned
 as `gs=[x, t₁,...,tₙ]`. (Note that these generators, although here denoted by the same symbols for simplicity, are isomorphic but not identical to 
-the generators `x, t₁,...,tₙ` of `C(x,t₁,...,tₙ)` given implicitely as the variables of the rational functions `Hᵢ`.)
+the generators `x, t₁,...,tₙ` of `C(x,t₁,...,tₙ)` given implicitly as the variables of the rational functions `Hᵢ`.)
 
 # Example  
 ```julia
 R, (x, t1, t2) = polynomial_ring(QQ, [:x, :t1, :t2])
 Z = zero(R)//1 # zero element of the fraction field of R
 K, gs, D = TowerOfDifferentialFields([t1//x, (t2^2+1)*x*t1 + Z])
 ```
-(Note: by adding `Z` to a polynomial we explicitely transform it to an element of the fraction field.)
+(Note: by adding `Z` to a polynomial we explicitly transform it to an element of the fraction field.)
 """
 function TowerOfDifferentialFields(Hs::Vector{F})  where 
     {T<:FieldElement, P<:MPolyRingElem{T}, F<:FracElem{P}}
@@ -164,8 +164,8 @@ end
 
 function tan2sincos(f::K, arg::SymbolicUtils.Symbolic, vars::Vector, h::Int=0) where 
     {T<:FieldElement, P<:PolyRingElem{T}, K<:FracElem{P}}
-    # This function transforms a Nemo/AbstractAlgebra rational funktion with
-    # varibale t representing tan(arg) to a SymbolicUtils expression which is
+    # This function transforms a Nemo/AbstractAlgebra rational function with
+    # variable t representing tan(arg) to a SymbolicUtils expression which is
     # a quotient in which both numerator and denominator are linear combinations
     # of expressions of the form cos(2*j*arg) or sin(2*j*arg) where j is an integer >=0.
     k = base_ring(base_ring(parent(f)))

src/methods/risch/parametric_problems.jl

@@ -983,7 +983,7 @@ function LimitedIntegrateReduce(f::F, ws::Vector{F}, D::Derivation) where
     # Note: LimitedIntegrateReduce seems to be the only algorithm in Bronstein's book,
     # where he messed something up. Already in equation (7.32) of Corollary 7.2.1 (p.247)
     # the coefficient of D(p) contains a factor hs too many. This then reproduces in the
-    # algoritm.
+    # algorithm.
     iscompatible(f, D) && all(iscompatible(w, D) for w in ws) || 
         error("rational functions f and w_i must be in the domain of derivation D")
     dn, ds = SplitFactor(denominator(f), D)

src/methods/risch/transcendental_functions.jl

@@ -175,8 +175,8 @@ function ConstantPart(ss::Vector{P}, Ss::Vector{PP}, D::Derivation) where  {P<:P
                         var = string(symbols(parent(Ss[i]))[1])
                         F = base_ring(ss[i])
                         if !iszero(u)
-                            # Ignore log terms with contstant arguments. In some cases the denominator of the constant argument
-                            # might be zero after substitutiong (u,v). So this avoids divison by zero in these cases.
+                            # Ignore log terms with constant arguments. In some cases the denominator of the constant argument
+                            # might be zero after substitutiong (u,v). So this avoids division by zero in these cases.
                             if degree(RT.LT.arg)>0 || (!isconstant(numerator(constant_coefficient(RT.LT.arg))(u,v), BaseDerivation(D)) &&
                                                        !isconstant(denominator(constant_coefficient(RT.LT.arg))(u,v), BaseDerivation(D)))
                                 # TODO: Think about avoiding division by zero like below for atan term.
@@ -187,12 +187,12 @@ function ConstantPart(ss::Vector{P}, Ss::Vector{PP}, D::Derivation) where  {P<:P
                             end
                         end
                         for AT in RT.ATs    
-                            # Ignore atan terms with contstant arguments. In some cases the denominator of the constant argument
-                            # might be zero after substitutiong (u,v). So this avoids divison by zero in these cases.
+                            # Ignore atan terms with constant arguments. In some cases the denominator of the constant argument
+                            # might be zero after substitutiong (u,v). So this avoids division by zero in these cases.
                             if degree(AT.arg)>0 || (!isconstant(numerator(constant_coefficient(AT.arg))(u,v), BaseDerivation(D)) &&
                                                     !isconstant(denominator(constant_coefficient(AT.arg))(u,v), BaseDerivation(D)))
                                 if all([!iszero(denominator(c)(u, v)) for c in coefficients(AT.arg)])
-                                    # Ignore atan term if substitution of (u,v) in argument would cause divion by zero. 
+                                    # Ignore atan term if substitution of (u,v) in argument would cause division by zero. 
                                     # This requires more thought, but it seems to work...
                                     g = polynomial(F, [numerator(c)(u, v)//denominator(c)(u, v) for c in coefficients(AT.arg)], var)
                                     push!(gs, FunctionTerm(atan, AT.coeff*v, g))
@@ -503,7 +503,7 @@ function InFieldDerivative(f::F, D::Derivation) where
             a0 = p1 - D(q2)
         else
             H = MonomialDerivative(D)
-            throw(NotImplementedError("InFieldDerivative: monomial deivative =$H\n@ $(@__FILE__):$(@__LINE__)"))
+            throw(NotImplementedError("InFieldDerivative: monomial derivative =$H\n@ $(@__FILE__):$(@__LINE__)"))
         end
         @assert isone(denominator(a0)) && degree(numerator(a0))<=0 # p-D(q) ∈ k
         a = constant_coefficient(numerator(a0))
@@ -681,7 +681,7 @@ function InFieldLogarithmicDerivativeOfRadical(f::F, D::Derivation; expect_one::
             U = v^div(N, m)*(u+Z)^div(N, n)*(t^2+1+Z)^div(e*N, n)
             return N, U, 1
         elseif iszero(real(a)) 
-            # Note: This case is not treated in 5.12 of Bronsteins's book, altough it seems
+            # Note: This case is not treated in 5.12 of Bronsteins's book, although it seems
             # to be the one relevant for checking the condition of Theorem 5.10.1.
             # I did not prove that in the case of Theorem 5.12 real(a)=0 always holds true.
             ai = imag(a)
@@ -690,7 +690,7 @@ function InFieldLogarithmicDerivativeOfRadical(f::F, D::Derivation; expect_one::
             if !isrational(c1) || !isrational(c2)
                 return no_solution
             end
-            # implicitely set u = 1 => D(u)//u = 0            
+            # implicitly set u = 1 => D(u)//u = 0            
             c1 = rationalize_over_Int(c1)
             c2 = rationalize_over_Int(c2)
             n = lcm(denominator(c1), denominator(c2))