Merge pull request #250 from abhro/patch-1

Minor documentation fixes

Author: ChrisRackauckas

docs/src/basics/SampledIntegralProblem.md

@@ -24,7 +24,7 @@ method = TrapezoidalRule()
 solve(problem, method)
 ```
 
-The exact answer is of course \$ 1/3 \$.
+The exact answer is of course ``1/3``.
 
 ## Details
 

docs/src/tutorials/numerical_integrals.md

@@ -125,7 +125,7 @@ For example, we can create our own sine function by integrating the cosine funct
 using Integrals
 my_sin(x) = solve(IntegralProblem((x, p) -> cos(x), (0.0, x)), QuadGKJL()).u
 x = 0:0.1:(2 * pi)
-@. my_sin(x) ≈ sin(x)
+all(@. my_sin(x) ≈ sin(x))
 ```
 
 ## Infinity handling

src/algorithms.jl

@@ -12,6 +12,7 @@ allocate the buffer as this is handled automatically.
 
 ## References
 
+```tex
 @article{laurie1997calculation,
 title={Calculation of Gauss-Kronrod quadrature rules},
 author={Laurie, Dirk},
@@ -21,6 +22,7 @@ number={219},
 pages={1133--1145},
 year={1997}
 }
+```
 """
 struct QuadGKJL{F, B} <: SciMLBase.AbstractIntegralAlgorithm
     order::Int
@@ -44,6 +46,7 @@ you do not allocate the buffer as this is handled automatically.
 
 ## References
 
+```tex
 @article{genz1980remarks,
 title={Remarks on algorithm 006: An adaptive algorithm for numerical integration over an N-dimensional rectangular region},
 author={Genz, Alan C and Malik, Aftab Ahmad},
@@ -54,6 +57,7 @@ pages={295--302},
 year={1980},
 publisher={Elsevier}
 }
+```
 """
 struct HCubatureJL{F, B} <: SciMLBase.AbstractIntegralAlgorithm
     initdiv::Int
@@ -81,6 +85,7 @@ This algorithm can only integrate `Float64`-valued functions
 
 ## References
 
+```tex
 @article{lepage1978new,
 title={A new algorithm for adaptive multidimensional integration},
 author={Lepage, G Peter},
@@ -91,6 +96,7 @@ pages={192--203},
 year={1978},
 publisher={Elsevier}
 }
+```
 """
 struct VEGAS{S} <: SciMLBase.AbstractIntegralAlgorithm
     nbins::Int
@@ -143,7 +149,7 @@ function GaussLegendre(; n = 250, subintervals = 1, nodes = nothing, weights = n
 end
 
 """
-QuadratureRule(q; n=250)
+    QuadratureRule(q; n=250)
 
 Algorithm to construct and evaluate a quadrature rule `q` of `n` points computed from the
 inputs as `x, w = q(n)`. It assumes the nodes and weights are for the standard interval

src/algorithms_extension.jl

@@ -13,6 +13,7 @@ Importance sampling is used to reduce variance.
 
 ## References
 
+```tex
 @article{lepage1978new,
 title={A new algorithm for adaptive multidimensional integration},
 author={Lepage, G Peter},
@@ -23,6 +24,7 @@ pages={192--203},
 year={1978},
 publisher={Elsevier}
 }
+```
 """
 struct CubaVegas <: AbstractCubaAlgorithm
     flags::Int
@@ -42,6 +44,7 @@ Importance sampling and subdivision are thus used to reduce variance.
 
 ## References
 
+```tex
 @article{hahn2005cuba,
 title={Cuba—a library for multidimensional numerical integration},
 author={Hahn, Thomas},
@@ -52,6 +55,7 @@ pages={78--95},
 year={2005},
 publisher={Elsevier}
 }
+```
 """
 struct CubaSUAVE{R} <: AbstractCubaAlgorithm where {R <: Real}
     flags::Int
@@ -70,6 +74,7 @@ Stratified sampling is used to reduce variance.
 
 ## References
 
+```tex
 @article{friedman1981nested,
 title={A nested partitioning procedure for numerical multiple integration},
 author={Friedman, Jerome H and Wright, Margaret H},
@@ -80,6 +85,7 @@ pages={76--92},
 year={1981},
 publisher={ACM New York, NY, USA}
 }
+```
 """
 struct CubaDivonne{R1, R2, R3, R4} <:
        AbstractCubaAlgorithm where {R1 <: Real, R2 <: Real, R3 <: Real, R4 <: Real}
@@ -105,6 +111,7 @@ Multidimensional h-adaptive integration from Cuba.jl.
 
 ## References
 
+```tex
 @article{berntsen1991adaptive,
 title={An adaptive algorithm for the approximate calculation of multiple integrals},
 author={Berntsen, Jarle and Espelid, Terje O and Genz, Alan},
@@ -115,6 +122,7 @@ pages={437--451},
 year={1991},
 publisher={ACM New York, NY, USA}
 }
+```
 """
 struct CubaCuhre <: AbstractCubaAlgorithm
     flags::Int
@@ -165,6 +173,7 @@ Defaults to `Cubature.INDIVIDUAL`, other options are
 
 ## References
 
+```tex
 @article{genz1980remarks,
 title={Remarks on algorithm 006: An adaptive algorithm for numerical integration over an N-dimensional rectangular region},
 author={Genz, Alan C and Malik, Aftab Ahmad},
@@ -175,6 +184,7 @@ pages={295--302},
 year={1980},
 publisher={Elsevier}
 }
+```
 """
 struct CubatureJLh <: AbstractCubatureJLAlgorithm
     error_norm::Int32

src/algorithms_sampled.jl

@@ -7,7 +7,7 @@ Struct for evaluating an integral via the trapezoidal rule.
 
 Example with sampled data:
 
-```
+```julia
 using Integrals
 f = x -> x^2
 x = range(0, 1, length=20)
@@ -28,7 +28,7 @@ Simpson's composite 1/3 rule for non-equidistant grids.
 
 Example with equidistant data:
 
-```
+```julia
 using Integrals
 f = x -> x^2
 x = range(0, 1, length=20)