mirror of
https://github.com/lcn2/calc.git
synced 2025-08-19 01:13:27 +03:00
convert ASCII TABs to ASCII SPACEs
Converted all ASCII tabs to ASCII spaces using a 8 character tab stop, for all files, except for all Makefiles (plus rpm.mk). The `git diff -w` reports no changes.
This commit is contained in:
Landon Curt Noll
58
help/poly
58
help/poly
@@ -8,65 +8,65 @@ SYNOPSIS
|
||||
TYPES
|
||||
For first case:
|
||||
|
||||
a, b, ... Arithmetic
|
||||
a, b, ... Arithmetic
|
||||
|
||||
x Arithmetic
|
||||
x Arithmetic
|
||||
|
||||
return Depends on argument types
|
||||
return Depends on argument types
|
||||
|
||||
For second case:
|
||||
|
||||
clist List of coefficients
|
||||
clist List of coefficients
|
||||
|
||||
x, y, ... Coefficients
|
||||
x, y, ... Coefficients
|
||||
|
||||
return Depends on argument types
|
||||
return Depends on argument types
|
||||
|
||||
Here an arithmetic type is one for which the required + and *
|
||||
operations are defined, e.g. real or complex numbers or square
|
||||
matrices of the same size. A coefficient is either of arithmetic
|
||||
matrices of the same size. A coefficient is either of arithmetic
|
||||
type or a list of coefficients.
|
||||
|
||||
DESCRIPTION
|
||||
If the first argument is not a list, and the necessary operations are
|
||||
defined:
|
||||
|
||||
poly(a_0, a_1, ..., a_n, x)
|
||||
poly(a_0, a_1, ..., a_n, x)
|
||||
|
||||
returns the value of:
|
||||
|
||||
a_n + (a_n-1 + ... + (a_1 + a_0 * x) * x ...) * x
|
||||
a_n + (a_n-1 + ... + (a_1 + a_0 * x) * x ...) * x
|
||||
|
||||
If the coefficients a_0, a_1, ..., a_n and x are elements of a
|
||||
commutative ring, e.g. if the coefficients and x are real or complex
|
||||
numbers, this is the value of the polynomial:
|
||||
|
||||
a_0 * x^n + a_1 * x^(n-1) + ... + a_(n-1) * x + a_n.
|
||||
a_0 * x^n + a_1 * x^(n-1) + ... + a_(n-1) * x + a_n.
|
||||
|
||||
For other structures (e.g. if addition is not commutative),
|
||||
the order of operations may be relevant.
|
||||
|
||||
In particular:
|
||||
|
||||
poly(a, x) returns the value of a.
|
||||
poly(a, x) returns the value of a.
|
||||
|
||||
poly(a, b, x) returns the value of b + a * x
|
||||
poly(a, b, x) returns the value of b + a * x
|
||||
|
||||
poly(a, b, c, x) returns the value of c + (b + a * x) * x
|
||||
poly(a, b, c, x) returns the value of c + (b + a * x) * x
|
||||
|
||||
|
||||
If the first argument is a list as if defined by:
|
||||
|
||||
clist = list(a_0, a_1, ..., a_n)
|
||||
clist = list(a_0, a_1, ..., a_n)
|
||||
|
||||
and the coefficients a_i and x are are of arithmetic type,
|
||||
poly(clist, x) returns:
|
||||
|
||||
a_0 + (a_1 + (a_2 + ... + a_n * x) * x)
|
||||
a_0 + (a_1 + (a_2 + ... + a_n * x) * x)
|
||||
|
||||
which for a commutative ring, expands to:
|
||||
|
||||
a_0 + a_1 * x + ... + a_n * x^n.
|
||||
a_0 + a_1 * x + ... + a_n * x^n.
|
||||
|
||||
If clist is the empty list, the value returned is the number 0.
|
||||
|
||||
@@ -78,36 +78,36 @@ DESCRIPTION
|
||||
to such an element is the value of poly for that list and the next
|
||||
argument in x, y, ... For example:
|
||||
|
||||
poly(list(list(a,b,c), list(d,e), f), x, y)
|
||||
poly(list(list(a,b,c), list(d,e), f), x, y)
|
||||
|
||||
returns:
|
||||
|
||||
(a + b * y + c * y^2) + (d + e * y) * x + f * x^2.
|
||||
(a + b * y + c * y^2) + (d + e * y) * x + f * x^2.
|
||||
|
||||
Arguments in excess of those required for clist are ignored, e.g.:
|
||||
|
||||
poly(list(1,2,3), x, y)
|
||||
poly(list(1,2,3), x, y)
|
||||
|
||||
returns the same as poly(list(1,2,3), x). If the number of
|
||||
arguments is less than greatest depth of lists in clist, the
|
||||
"missing" arguments are deemed to be zero. E.g.:
|
||||
"missing" arguments are deemed to be zero. E.g.:
|
||||
|
||||
poly(list(list(1,2), list(3,4), 5), x)
|
||||
poly(list(list(1,2), list(3,4), 5), x)
|
||||
|
||||
returns the same as:
|
||||
|
||||
poly(list(1, 3, 5), x).
|
||||
poly(list(1, 3, 5), x).
|
||||
|
||||
If in the clist case, one or more of x, y, ... is a list, the
|
||||
arguments to be applied to the polynomial are the successive
|
||||
non-list values in the list or sublists. For example, if the x_i
|
||||
are not lists:
|
||||
|
||||
poly(clist, list(x_0, x_1), x_2, list(list(x_3, x_4), x_5))
|
||||
poly(clist, list(x_0, x_1), x_2, list(list(x_3, x_4), x_5))
|
||||
|
||||
returns the same as:
|
||||
|
||||
poly(clist, x_0, x_1, x_2, x_3, x_4, x_5).
|
||||
poly(clist, x_0, x_1, x_2, x_3, x_4, x_5).
|
||||
|
||||
EXAMPLE
|
||||
; print poly(2, 3, 5, 7), poly(list(5, 3, 2), 7), 5 + 3 * 7 + 2 * 7^2
|
||||
@@ -144,7 +144,7 @@ SEE ALSO
|
||||
##
|
||||
## Calc is distributed in the hope that it will be useful, but WITHOUT
|
||||
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
|
||||
## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
|
||||
## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
|
||||
## Public License for more details.
|
||||
##
|
||||
## A copy of version 2.1 of the GNU Lesser General Public License is
|
||||
@@ -152,8 +152,8 @@ SEE ALSO
|
||||
## received a copy with calc; if not, write to Free Software Foundation, Inc.
|
||||
## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
|
||||
##
|
||||
## Under source code control: 1995/12/02 02:40:43
|
||||
## File existed as early as: 1995
|
||||
## Under source code control: 1995/12/02 02:40:43
|
||||
## File existed as early as: 1995
|
||||
##
|
||||
## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
|
||||
## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
|
||||
## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
|
||||
## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
|
||||
|
||||
Reference in New Issue
Block a user