Main functions

The keys redefined by 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 +, -, *, /, y^x, $\sqrt{x}$, $\pm$, 1/x, $\partial$, $\int$ 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 $\alpha$-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.

Remark 1   A main menu of the HP48GX is available by hitting the PRG key and may be useful for beginners. Note that the former MTH and PRG key definition are reached by $\alpha$-right shift-MTH or $\alpha$-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 $\alpha$-right shift followed by the number of the topic in the MTH-Erable menu. For example, if you hit $\alpha$-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):
  $\frac{(X+1)^4}{X^2-1}$ EXPA $\frac{X^3+3X^2+3X+1}{X-1}$
• COLC (factorize an expression):
  X⁴-1 COLC (X²+1)(X+1)(X-1)
• der1 (derive an expression with respect to the current variable):
  $\ln(\ln(X))^2$ der1 $2\frac{1}{X}\frac{1}{\ln(X)}\ln(\ln(X))$
• RISCH (integrate an expression with respect to the current variable):
  $e^X \sin(X)^2$ RISCH $e^X\frac{1}{2}+e^X((-\sin(2X)\frac{1}{5} +\frac{-1}{10}\cos(2X))$
• LIMIT (of the expression at stack level 2, you must specify the variable and the limit point at level 1, e.g. 'X=0'):
  $(1+\frac{1}{X} )^X$, $X=\infty$ LIMIT e
• TAYLR (the built-in one):
  $\sin(X)$, X 4 TAYLR $X-\frac{1}{3!} X^3$
• EXEC (to make a substitution at stack level 2, you must specify the substitution at level 1, e.g. 'X=1+Y'):
  $\ln(X^2+1)+\arctan(X)$, X=2 EXEC $\ln(2^2+1)+\arctan(2)$
• SOLV (to isolate a variable at level 1 in an expression at level 2):
  X⁴-1, X SOLV X, { 1 -1 'i' '-i' }
• FSIGN (sign of a rational fraction):
  X²-X-2 FSIGN returns 'X': { + 1 - 2 + }. You read the sign starting from $-\infty$ at the left to $+\infty$ 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):
  $\int _1^2 \ln(X) dX$, X IPP $\int _1^2 \ln(X)\ dX=2\ln(2)-\int _1^2 1 \ dX$
  (applies $\int uv' =[uv]-\int u'v$ where $\ln(X)$ is the function u and the argument X is the function v)

Some of these commands are directly assigned to a shortcut:

• the EXPA command is assigned to the $\alpha$-right shift-SPC sequence,
• the EXEC command is assigned to the $\alpha$-right shift-EVAL sequence,
• i is assigned to the CST key,
• X is assigned to the DEL key,
• $\infty$ or $+\infty$ is assigned to the $\alpha$-right shift-DEL sequence,
• $-\infty$ is assigned to the $\alpha$-left shift-DEL sequence,

Here is a brief description of all the functions of Erable which may be launched this way:

• $\alpha$-right shift-1: basic algebra commands:
  EXPA, COLC, der1, RISCH, LIMIT, TAYLR, EXEC, SOLV, FSIGN, IPP (see above)
• $\alpha$-right shift-2: complex:
  re, im, conj, arg, abs and i. Note that you can always get i if you hit the CST key.
• $\alpha$-right shift-3: trigonometry:
  TEXPA (trigonometric expand), TRIGLIN (trig. linearization), SINCOS (convert complex $\exp$ and $\ln$ to trigonometric expressions), TRIG (applies $\sin^2+\cos^2=1$ 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 $\tan$ of the half-angle), ->SC2 (convert $\tan$ to $\sin$ and $\cos$ of the double angle), T->SC (convert $\tan$ to $\sin$ and $\cos$ of the same angle).
• $\alpha$-right shift-4: matrices
  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.
• $\alpha$-right shift-5, conversions:
  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)
• $\alpha$-right shift-6, integer and polynomial arithmetic:
  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 ( $\left(\begin{array}{c} n \\ p \end{array}\right)$).
• $\alpha$-right shift-7, solve and factorization:
  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)
• $\alpha$-right shift-8, exponentials and logarithms:
  EXPLIN (linearization of exponentials), EXPLN (convert sines and cosines to exponentials), LNCOLC (collect logarithms), TEXPA (expand logarithms and exponentials), TSIMP (transcendental presimplification)
• $\alpha$-right shift-9, differential calculus:
  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 $\alpha$-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 $\alpha$-right shifted:

• On SX models, the $\rightarrow$Q and $\rightarrow$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.
• On a G/GX models, use $\alpha$ - -Q or $\rightarrow$NUM (not shifted).