| Type: | Package |
| Title: | Generating 'Sweave' Code for 'R/exams' Questions in Mathematics |
| Version: | 0.1.2 |
| Description: | When using the R package 'exams' to write mathematics questions in 'Sweave' files, the output of a lot of R functions need to be adjusted for display in mathematical formulas. Specifically, the functions were accumulated when writing questions for the topics of the mathematics courses College Algebra, Precalculus, Calculus, Differential Equations, Introduction to Probability, and Linear Algebra. The output of the developed functions can be used in 'Sweave' files. |
| Depends: | numbers, fractional, pracma, polynom |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.2.3 |
| NeedsCompilation: | no |
| Packaged: | 2023-05-11 14:16:21 UTC; Hu |
| Author: | Qingwen Hu  [aut,
cre, cph] |
| Maintainer: | Qingwen Hu <huqwen@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2023-05-12 14:20:02 UTC |
Apply the Gram-Schmidt process to orthogonize a group of 3 vectors
Description
Apply the Gram-Schmidt process to convert the group of 3 vectors (x,y,z) into an orthogonal group (u,v,w) without normalizing to unit vectors. The output is a matrix with columns (u,v,w).
Usage
G3S(x,y,z)
Arguments
x, y, z |
a group of 3 vectors (x,y,z) |
Details
Need the one dimensional projection function 'myGS' from the same package.
Value
The output is a matrix with columns (u,v,w) which are an orthogonal set of vectors.
See Also
Examples
G3S(c(1,2,3),c(3,2,1),c(4,5,9))
fractional(G3S(c(1,2,3),c(3,2,1),c(4,5,9)))
Rational number sequence to polynomial in TeX code
Description
The function 'polynomial' in the 'polynom' package converts a sequence of rational numbers into a polynomial with decimal coefficients. This function 'c2p' converts the output of 'polynomial' into the TeX form of a polynomial where coefficients are of vertical fraction form using the package 'fractional'.
Usage
c2p(m)
Arguments
m |
a list of rational numbers which are coefficients of a polynomial in descending order. |
Details
The function uses 'polynomial' function from the package 'polynom' which defaults the polynomial in ascending order.
Value
The function returns a string of TeX code of the polynomial with rational coefficients.
See Also
Examples
m <- sample(c(1:100),5)
m
c2p(m)
Sequence of rational numbers into comma separated string
Description
Convert a sequence of rational numbers into a string separated with a comma where the fractions are in backslash form.
Usage
c2str(x)
Arguments
x |
a list of rational numbers. |
Details
The output string was originally designed for 'string' type answers of 'R/exams' when a sequence of rational numbers are the answers from multiple parts of the question.
Value
The output is a string of rational numbers with backslash denoting division.
See Also
Examples
x <- sample(c(1:100),5)/100
x
c2str(x)
Sequence of numbers into a string of TeX code with plus minus signs.
Description
Convert a sequence of numbers into a string of TeX code for the sequence with plus minus signs for each number of the sequence, where the fractions are in vertical form.
Usage
c2strpm(x)
Arguments
x |
a list of rational numbers. |
Value
The output is a string of rational numbers with backslash denoting division and plus minus signs in front of each number.
See Also
Examples
x <- sample(c(1:100),5)
x
c2strpm(x)
Convert a matrix into a comma separated string.
Description
The output of cm2l is a vector of strings with length equal to the column size of the input matrix. The i-th entry is the string of the numbers from the i-th column of the matrix. For example, the 2 by 2 identity matrix is converted into c("1,0", "0,1").
Usage
cm2l(matrix)
Arguments
matrix |
a matrix. |
Value
a vector of the strings of the columns of x. Each entry is a string of the column.
See Also
Examples
a <- matrix(sample(c((-10):10),12),nrow =3,byrow=TRUE)
cm2l(a)
Triangle leg values to TeX code of the cosine value
Description
Convert a cosine value into TeX code with simplification on the radical from the hypotenuse, where the input (a,b) are the integer lengths of the legs of the right triangle with a the vertical leg, b the horizontal leg. The simplification is provided by another function 'simpRad' in the same package.
Usage
costex(a,b)
Arguments
a |
The vertical length of the right triangle, which can be negative. |
b |
The horizontal length of the right triangle, which can be negative. |
Details
Given integer lengths of a the legs of a triangle, the function returns a string of tex code for the value of the associated cosine.
Value
The function returns a string of TeX code for the value of the associated cosine.
Note
Caution: Integer coordinates (x,y) in the plane should switch order to be the input (y,x) of the function.
See Also
Examples
a <- sample(c(1:5),1)
b <- sample(c(1:5),1)
costex(a,b)
Display the cycle notation of the permutation
Description
Display the cycle notation of the permutation using the output matrix of the function permucycle().
Usage
cycledisplay(x)
Arguments
x |
output matrix of the function 'permucycle'. |
Value
A cycle notation of a permutation.
See Also
Examples
cycledisplay(permucycle(c(3,2,1)))
paste0(cycledisplay(permucycle(c(3,2,1))),collapse ="")
Delete the first zero in the output remainder of 'polydiv'
Description
The output remainder of polydiv(x,y)[2] from the package 'pracma' may contain a zero in the first place which is not needed for text presentation. The function will modify the output by deleting the first zero, if any.
Usage
delzero(x)
Arguments
x |
a list of numbers whose first entry may be zero or close to zero with absolute value less than or equal to 1e-10. |
Value
The function truncates the first zero entry of the list.
Examples
x <- c(0,sample(c((-10):10),5))
delzero(x)
Convert a decimal number into exactly 4 decimal places.
Description
Convert a decimal number into exactly 4 decimal places without scientific notation.
Usage
fmt4(x)
Arguments
x |
a decimal number. |
Details
Round a decimal number into exactly 4 decimal places without scientific notation.
Value
A decimal number rounded into exactly 4 decimal places.
See Also
Examples
x <- sin (sample(c(1:5),1))
fmt4(x)
Convert a decimal number into exactly n decimal places.
Description
Convert a decimal number into exactly n decimal places without scientific notation.
Usage
fmtN(x,n)
Arguments
x, n |
where x is a decimal number and n is the numbers of decimal places to keep. |
Details
Round a decimal number into exactly n decimal places.
Value
A decimal number rounded into exactly n decimal places.
See Also
fmt4 is a special case of fmtN but is simpler to use with one argument.
Examples
x <- sin (sample(c(1:5),1))
n <- sample(c(4:10),1)
fmtN(x,n)
TeX code of the hypotenuse
Description
Given the lengths of the integer legs of a right triangle, the function generates the TeX code of the length of the hypotenuse in simplified form.
Usage
hypotex(a,b)
Arguments
a, b |
a pair of the integer leg lengths of a right triangle. |
Value
The function generates the TeX code of the hypotenuse in simplified form of the radicals.
See Also
Examples
a <- sample(c(1:5),1)
b <- sample(c(1:5),1)
hypotex(a,b)
Count the number of total inversions of a permutation
Description
inversions() counts the number of inversions of a permutation.
Usage
inversions(x)
Arguments
x |
a permutation of 1, 2, ..., n. |
Details
Input must be a list of numbers.
Value
The total number of inversions in a list.
See Also
Examples
inversions(c(3,1,2))
Generating a vector of inversions for a permutation
Description
inversionv() returns the vector of inversions for each entry in the permutation. For example, inversionv(1,2,0) = (1,1,0), inversionv(0,1,2) = (0,0,0).
Usage
inversionv(x)
Arguments
x |
a list of numbers, or a permutation. |
Value
inversionv returns a vector of inversions for each member of the permutation.
See Also
Examples
inversionv(c(3,1,2,4))
Converting a matrix into TeX code of a matrix without brackets
Description
m22l converts a matrix into a matrix without brackets or parentheses around the array of numbers.
Usage
m22l(matrix)
Arguments
matrix |
a matrix. |
Value
array a numbers without parentheses.
See Also
Examples
a <- matrix(sample(c(-10:10),12),nrow =3,byrow=TRUE)
m22l(a)
Converting a matrix into TeX code of a matrix with square brackets
Description
m2l converts a matrix into TeX code with square brackets.
Usage
m2l(matrix)
Arguments
matrix |
a matrix |
Value
TeX code of the matrix in 'Sweave' file.
See Also
Examples
a <- matrix(sample(c(-10:10),12),nrow =3,byrow=TRUE)
m2l(a)
Convert multiple decimals into tex code of vertical fractions
Description
The function converts multiple decimals into tex code of vertical fractions.
Usage
mfrac(z)
Arguments
z |
a list of decimal numbers. |
Value
The function returns a string of tex code for the numbers in vertical fraction form.
Note
The function used function 'rfrac' in the same package which depends on the package 'fractional'.
See Also
Examples
z <- sample(c(1:55),6)/100
mfrac(z)
Orthogonal projection of y onto x
Description
Orthogonal projection of y onto x.
Usage
myGS(x,y)
Arguments
x, y |
a pairs of vectors. |
Value
myGS returns a vector of the projection of y onto x.
See Also
Examples
x <- sample(c((-10):10),3)
y <- sample(c((-10):10),3)
myGS(x,y)
fractional(myGS(x,y))
Lists permutations of a vector with distinct entries
Description
perm(v) lists permutations of a vector v with distinct entries. The output is a matrix with each row a permutation. It cannot distinguish identical permutations.
Usage
perm(v)
Arguments
v |
is a vector with distinct entries. |
Value
an n! by n matrix with each row a permuation of the enties of v.
See Also
permucycle, permuorder,cycledisplay
Examples
x <- sample(c((-10):10),3)
perm(x)
Matrix representation of the cycles of a permutation.
Description
permucycle returns a matrix containing information of a permutation. See the Value section for details.
Usage
permucycle(x)
Arguments
x |
a permutation |
Value
Given a permutation x of the numbers 1, 2, ..., n, and i with value from 1 to n. permucycle() returns a (n+1) by (n+1) matrix A with
A[1, 1] |
the total number of cycles |
A[(i+1), 1] |
the length of the i-th cycle |
A[(i+1), 2:(n+1)] |
the members of the i-th cycle |
For example, permucycle(c(3,2,1)) will produce the following matrix:
[,1] [,2] [,3] [,4]
[1,] 2 0 0 0
[2,] 2 1 3 0
[3,] 1 2 0 0
[4,] 0 0 0 0
The 2 in the first row means there are two cycles; The second row means there is a cycle of length 2, with members (1,3); The third row means there is a cycle of length 1, with member (2); The fourth row is redundant for this specific case. One can read from the output of permucycle() to obtain cycle notation (13)(2) of the permutation, and other information.
See Also
Examples
permucycle(c(3,2,1))
Order of permutation
Description
Computing the order of the permutation x of the numbers 1, 2, ..., n, using the first column of the output matrix of the function 'permucycle', whose first entry N = permucycle()[1,1] is the total number of the cycles in the permutation, and permucycle()[2:(n+1),1] are the lengths of each cycle. Note: Since matrix can be regarded as a 1 dimensional vector with each column attached with the previous one, the argument of permuorder() can be the whole output of permucycle() when permuorder() just uses the first N+1 entries in the first column. Certainly specifying the first column of permucycle() to be the input will save some memory usage.
Usage
permuorder(x)
Arguments
x |
output matrix of the function permucycle() |
Value
The order of the permutation, which is the least common multiple of the orders of each contained cycle.
See Also
Examples
permuorder(permucycle(c(3,1,2)))
TeX code for positivity of randomized values
Description
Produce the TeX code of positivity of randomaized values.
Usage
pos(x)
Arguments
x |
a numeric number. |
Value
The function returns one of the symbols "<0", ">0", or "=0".
See Also
Examples
x <- sample(c((-10):10),1)
pos(x)
Converting a matrix into a comma separated string
Description
The output of rcm2l is a vector of strings with length equal to the row size of the input matrix. The i-th entry is the string of the numbers from the i-th row of the matrix. For example, the standard 2 by 2 Jordan block with 2 in the main diagonal is converted into c("2,1", "0,2").
Usage
rcm2l(matrix)
Arguments
matrix |
a matrix |
Value
a vector of strings with length equal to the row size of the input matrix. The i-th entry is the string of the numbers from the i-th row of the matrix.
See Also
Examples
a <- matrix(sample(c(-10:10),12),nrow =3,byrow=TRUE)
rcm2l(a)
Convert a decimal into TeX code of vertical fractions
Description
The function converts a decimal into TeX code of vertical fractions, using functions 'denominators' and 'numerators' from the package 'fractional'.
Usage
rfrac(x)
Arguments
x |
a list of decimal numbers. |
Value
The function returns a string of TeX code for the number in vertical fraction form.
Note
The function depends on the package 'fractional'.
See Also
Examples
x <- sample(c(1:55),1)/100
rfrac(x)
Convert a decimal into TeX code of vertical fractions with the sign in front of the fraction
Description
The function converts a decimal into TeX code of vertical fractions, using functions 'denominators' and 'numerators' from the packaege 'fractional'. This function differs from 'rfrac' only in the place of the negative signs. 'rfracF' returns the fraction with the sign in front.
Usage
rfracF(x)
Arguments
x |
a list of decimal numbers. |
Value
The function returns a string of tex code for the number in vertical fraction form with the sign in front of the fraction.
Note
The function depends on the package 'fractional'.
See Also
Examples
x <- sample(c(1:55),1)/100
rfrac(x)
Convert a matrix into its transpose in TeX code
Description
rm2l converts a matrix into its transpose in TeX code.
Usage
rm2l(matrix)
Arguments
matrix |
a matrix. |
Value
It return the transpose of the input matrix in latex code.
See Also
Examples
a <- matrix(sample(c((-10):10),12),nrow =3,byrow=TRUE)
rm2l(a)
Show minus sign in front of fractions
Description
The minus sign in fractions should be in front of the fraction for display purpose, while many numerical algorithms may produce fractions with minus sign in the numerator. This function modifies the output of those packages into the correct display form in TeX code.
Usage
signF(a)
Arguments
a |
a numeric number. |
Value
The function returns one of the symbols "-" for negative numbers, or empty "" for nonnegative ones.
See Also
Examples
a <- sample(c((-10):10),1)/100
signF(a)
Simplify square roots of positive integers
Description
SimpRad uses the package 'numbers' to simplify square roots of positive integers.
Usage
simpRad(n)
Arguments
n |
a positive integer. |
Value
The function returns a string of TeX code for radical in simplified form.
Note
The function used functions 'primFactors' and 'radical' from the package of 'numbers'.
See Also
radical, primeFactors
Examples
n <- sample(c(4:100),1)
simpRad(n)
Triangle leg values to TeX code of the cosine value
Description
Convert a sine value into TeX code with simplification on the radical from the hypotenuse, where the input (a,b) are the integer lengths of the legs of the right triangle with a the vertical leg, b the horizontal leg. The simplification is provided by another function 'simpRad' in the same package.
Usage
sintex(a,b)
Arguments
a |
The vertical length of the right triangle, which can be negative. |
b |
The horizontal length of the right triangle, which can be negative. |
Details
Given integer lengths of the legs of a triangle, the function returns a string of TeX code for the value of the associated sine.
Value
The function returns a string of TeX code for the value of the associated sine.
Note
Caution: Integer coordinates (x,y) in the plane should switch order to be the input (y,x) of the function.
See Also
Examples
a <- sample(c(1:5),1)
b <- sample(c(1:5),1)
sintex(a,b)
Convert multiple decimals into TeX code of back slash fractions
Description
The function converts multiple decimals into TeX code of back slash fractions.
Usage
smfrac(z)
Arguments
z |
a list of decimal numbers. |
Value
The function returns a string of TeX code for the numbers in back slash fraction form.
Note
The function used function 'rfrac' in the same package which depends on the package 'fractional'.
See Also
Examples
z <- sample(c(1:55),6)/100
smfrac(z)