Erable
are most of the time preceded by the
and right-shift keys. For example, the add
addition function of
Erable
is obtained in USER
mode by hitting threes keys:
,
,
.
The same method applies for other arithmetic operations. The
+, -, *, /, yx, ,
,
1/x, ,
keys
are redefined (after
and
)
as add
, SUBT
, MULT
, DIV1
, POWER
,
SQRT
, CHS
, INVL
, der1
, RISCH
. These
commands are Erable
commands for addition, subtraction,
multiplication, division, power, square root, change sign, derivation and
integration with respect to the current variable 1.
All other Erable
functions may be reached by the MTH
-Erable
menu2
or by a key preceded by -right shift.
To launch the MTH
-Erable menu,
type the MTH
key, use arrow keys or
hit a number to select a topic and type the ENTER
key.
After that you select the desired command by hitting the white A
-F
keys or search further by hitting the NXT
key.
PRG
key
and may be useful for beginners. Note that the former MTH
and
PRG
key definition are reached by -right shift-MTH
or -right shift-PRG
. If you want to delete the PRG
key assignement, type 22.1 DELKEYS
(note that the 0.BACK
option
of the MTH
menu will no longer work)
You can directly reach a topic of Erable
by hitting -right
shift followed by the number of the topic in the MTH
-Erable menu.
For example, if you hit -right shift-1, you will get the
BASE ALGEBRA
menu, that is the most useful commands of Erable
that are illustrated with an example below:
EXPA
(expand an expression):
EXPA
COLC
(factorize an expression):
COLC
(X2+1)(X+1)(X-1)
der1
(derive an expression with respect to the
current variable):
der1
RISCH
(integrate an expression with respect to the current
variable):
RISCH
LIMIT
(of the expression at stack level 2, you must
specify the variable and the limit point at level 1, e.g. 'X=0'
):
LIMIT
e
TAYLR
(the built-in one):
TAYLR
EXEC
(to make a substitution at
stack level 2, you must specify the substitution at level 1, e.g.
'X=1+Y'
):
EXEC
SOLV
(to isolate a variable at level 1 in
an expression at level 2):
SOLV
X, { 1 -1 'i' '-i' }
FSIGN
(sign of a rational fraction):
FSIGN
returns 'X': { + 1 - 2 + }
. You read
the sign starting from
at the left to
at the
right. 1 and 2 are here zeroes from the rational fraction, in general
the value appearing in the list are roots or poles.
IPP
(integration by part: see 7.3):
IPP
EXPA
command is assigned to the
-right shift-SPC
sequence,
EXEC
command is assigned to the
-right shift-EVAL
sequence,
CST
key,
DEL
key,
DEL
sequence,
DEL
sequence,
Here is a brief description of all the functions of Erable
which may
be launched this way:
EXPA
, COLC
, der1
,
RISCH
, LIMIT
,
TAYLR
, EXEC
, SOLV
, FSIGN
,
IPP
(see above)
re
, im
, conj
, arg
, abs
and i. Note
that you can always get i if you hit the CST
key.
TEXPA
(trigonometric expand), TRIGLIN
(trig. linearization),
SINCOS
(convert complex
and
to trigonometric expressions),
TRIG
(applies
to simplify an expression),
TRIGCOS
(same as TRIG
, returns only cosines if possible),
TRIGSIN
(same as TRIGCOS
but returns only sines if possible),
HALFTAN
(convert to
of the half-angle), ->SC2
(convert
to
and
of the double angle),
T->SC
(convert
to
and
of the same angle).
rref
(row reduction to echelon form), JORDAN
(diagonalization
of matrices), det
(determinant), PCAR
(characteristic
polynomial), SYST
(solves a linear system), SOLGEN
(returns
all solutions of a linear system), RDET
(determinant by row
reduction), RANG
(half-row reduction), idn
(symbolic identity
matrix), LCXM
(to build a matrix), HILBERT
and VAND
to build Hilbert and Vandermonde matrices.
AXL
(numeric to symbolic matrices or conversely),
EXEC
(substitution), SINCOS
(exponentials and logarithms to sines and cosines), EXPLN
(sines
and cosines to exponentials), FXND
(fraction to numerator and
denominator or equality to left and right handsides), NDXF
(numerator and denominator to fraction), AXQ
and QXA
(matrix to symbolic representation of quadratic forms and conversely)
DIV2
(euclidean division), GDC1
(usual greatest common
denominator), GCD3
(extended gcd),
ABCUV
(Bézout identity), LCM1
(least
common multiple), PF
(partial fraction decomposition),
COLC
(factorization), DIVIS
(list of divisors),
SIMP2
(simplification of stack levels 2 and 1), EULER
(Euler indicatrix), fact
(factorial), comb
(
).
FROOTS
(roots and poles of a fraction with multiplicity),
FCOEF
(reverse of FROOTS
), SOLV
(isolate a variable
in an equation), LNCOLC
(collect logarithms), COLC
(factorization), EXEC
(substitution)
EXPLIN
(linearization of exponentials), EXPLN
(convert sines
and cosines to exponentials), LNCOLC
(collect logarithms), TEXPA
(expand logarithms and exponentials), TSIMP
(transcendental
presimplification)
der
(derivative and gradient), RISCH
(integration),
IPP
(integration by part), SERIES
(asymptotic series
expansion), LIMIT
(limits), DSOLVE
(ordinary first order
differential equation solver), LDEC
(linear differential equation
with constant coefficients solver), LAP
(Laplace transform),
ILAP
(invert Laplace transform)
An easy way to configure Erable
is to type the
-right shift-CST
sequence (for Erable
MODES
)
and select the mode you want to switch to.
Let's finish by redefined keys which are not -right shifted:
Q
and
NUM
keys (not alpha shifted) are redefined to handle matrices.
They toggle user flags 12, 14 and 15 (XNUM
to clear and XQ
to set) and system flag 2.
Q
or
NUM
(not shifted).