Texas Instruments TINSPIRE Reference Guide - Page 83

Q, propFrac, Catalog &gt

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propFrac( ) propFrac(Value1[, Var]) ⇒ value propFrac(rational_number) returns rational_number as the sum of an integer and a fraction having the same sign and a greater denominator magnitude than numerator magnitude. propFrac(rational_expression,Var) returns the sum of proper ratios and a polynomial with respect to Var. The degree of Var in the denominator exceeds the degree of Var in the numerator in each proper ratio. Similar powers of Var are collected. The terms and their factors are sorted with Var as the main variable. If Var is omitted, a proper fraction expansion is done with respect to the most main variable. The coefficients of the polynomial part are then made proper with respect to their most main variable first and so on. You can use the propFrac() function to represent mixed fractions and demonstrate addition and subtraction of mixed fractions. Catalog > Q QR Catalog > QR Matrix, qMatrix, rMatrix[, Tol] Calculates the Householder QR factorization of a real or complex matrix. The resulting Q and R matrices are stored to the specified Matrix. The Q matrix is unitary. The R matrix is upper triangular. The floating-point number (9.) in m1 causes results to be calculated in floating-point form. Optionally, any matrix element is treated as zero if its absolute value is less than Tol. This tolerance is used only if the matrix has floatingpoint entries and does not contain any symbolic variables that have not been assigned a value. Otherwise, Tol is ignored. /· • If you use or set the Auto or Approximate mode to Approximate, computations are done using floatingpoint arithmetic. • If Tol is omitted or not used, the default tolerance is calculated as: 5EL14 ·max(dim(Matrix)) ·rowNorm(Matrix) The QR factorization is computed numerically using Householder transformations. The symbolic solution is computed using GramSchmidt. The columns in qMatName are the orthonormal basis vectors that span the space defined by matrix. TI-Nspire™ Reference Guide 77

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TI-Nspire™ Reference Guide
77
Q
propFrac()
Catalog >
propFrac(
Value1
[
,
Var
]
)
⇒
value
propFrac(
rational_number
)
returns
rational_number
as the sum
of an integer and a fraction having the same sign and a greater
denominator magnitude than numerator magnitude.
propFrac(
rational_expression
,
Var
)
returns the sum of proper
ratios and a polynomial with respect to
Var
. The degree of
Var
in the
denominator exceeds the degree of
Var
in the numerator in each
proper ratio. Similar powers of
Var
are collected. The terms and their
factors are sorted with
Var
as the main variable.
If
Var
is omitted, a proper fraction expansion is done with respect to
the most main variable. The coefficients of the polynomial part are
then made proper with respect to their most main variable first and so
on.
You can use the
propFrac()
function to represent mixed fractions
and demonstrate addition and subtraction of mixed fractions.
QR
Catalog >
QR
Matrix
,
qMatrix
,
rMatrix
[
,
Tol
]
Calculates the Householder QR factorization of a real or complex
matrix. The resulting Q and R matrices are stored to the specified
Matrix
. The Q matrix is unitary. The R matrix is upper triangular.
Optionally, any matrix element is treated as zero if its absolute value
is less than
Tol
. This tolerance is used only if the matrix has floating-
point entries and does not contain any symbolic variables that have
not been assigned a value. Otherwise,
Tol
is ignored.
•
If you use
/·
or set the
Auto or Approximate
mode to Approximate, computations are done using floating-
point arithmetic.
•
If
Tol
is omitted or not used, the default tolerance is calculated
as:
5E
L
14
·
max(dim(
Matrix
))
·
rowNorm(
Matrix
)
The floating-point number (9.) in m1 causes results to be
calculated in floating-point form.
The QR factorization is computed numerically using Householder
transformations. The symbolic solution is computed using Gram-
Schmidt. The columns in
qMatName
are the orthonormal basis
vectors that span the space defined by
matrix
.