Line Editing Commands While authoring an expression, the text can be edited using the following line edit commands: Cursor movement commands: Ctrl-S move left a character Ctrl-D move right a character Ctrl-A move left a word Ctrl-F move right a word Ctrl-Q S move to left end of line Ctrl-Q D move to right end of line Text deletion commands: Ctrl-H Backspace delete char left of cursor Ctrl-G Del delete char at the cursor Ctrl-T delete word beginning at cursor Ctrl-Y delete whole line Ctrl-Q Y delete right end of line Ctrl-Q H delete left end of line Miscellaneous commands: Ctrl-M Enter enter line of text Ctrl-J Ctrl-Enter enter and simplify line of text Esc abort edit and return to menu Ctrl-V Ins toggle insert/overwrite modes Ctrl-U insert previous line of text F3 insert highlighted expression F4 insert highlighted expression enclosed in parentheses On PC compatible computers, the following Greek letters can be entered by holding down the Alt key while pressing the corresponding Latin (English) letter: Alt-A alpha Alt-M mu Alt-B beta Alt-P pi Alt-G Gamma Alt-S sigma Alt-D delta Alt-T tau Alt-N epsilon Alt-F Phi Alt-H Theta Alt-O Omega On PC compatible computers, the following mathematical constants and functions can be entered by holding down the Alt key while pressing the corresponding letter: Alt-E #e base of the natural logs Alt-I #i square root of -1 Alt-Q SQRT square root function Functions, Constants, and Operators Derive knows how to approximate and/or simplify the following mathematical functions, constants, and operators. In approximate mode and given numeric arguments, they are approximated numerically to the current precision level. Otherwise they are simplified algebraically using powerful transformations. Many transformations are applied automatically; some are applied only when you request them by issuing a Manage command. Constants: #e base of the natural logarithms #i square root of -1 pi circle's circumference to diameter ratio deg radians per degree inf positive infinity Operators (page 17): - z minus z z + w z plus w z - w z minus w z * w z times w z w z times w z / w z divided by w z ^ w z raised to the power w z % z percent = z/100 z ! z factorial Exponential functions (page 71): #e base of the natural logarithms EXP (z) #e raised to the power z SQRT (z) square root of z Logarithmic functions (page 72): LN (z) natural log of z LOG (z) natural log of z LOG (z, w) log of z to the base w Trigonometric functions (page 73): pi circle's circumference to diameter ratio deg radians per degree SIN (z deg) sine of z degrees SIN (z) sine of z radians COS (z) cosine of z radians TAN (z) tangent of z radians COT (z) cotangent of z radians SEC (z) secant of z radians CSC (z) cosecant of z radians Inverse trigonometric functions (radians) (page 75): ASIN (z) angle whose sine is z ACOS (z) angle whose cosine is z ATAN (z) angle whose tangent is z ACOT (z) angle whose cotangent is z ATAN (y, x) angle of the point (x,y) ACOT (x, y) angle of the point (x,y) ASEC (z) angle whose secant is z ACSC (z) angle whose cosecant is z Hyperbolic functions (page 76): SINH (z) hyperbolic sine of z COSH (z) hyperbolic cosine of z TANH (z) hyperbolic tangent of z COTH (z) hyperbolic cotangent of z SECH (z) hyperbolic secant of z CSCH (z) hyperbolic cosecant of z Inverse hyperbolic functions (page 76): ASINH (z) inverse hyperbolic sine of z ACOSH (z) inverse hyperbolic cosine of z ATANH (z) inverse hyperbolic tangent of z ACOTH (z) inverse hyperbolic cotangent of z ASECH (z) inverse hyperbolic secant of z ACSCH (z) inverse hyperbolic cosecant of z Piecewise continuous functions (page 76): ABS (x) absolute value of z SIGN (x) sign of z MAX (x, y, ...) maximum of arguments MIN (x, y, ...) minimum of arguments STEP (x) 1 if x>0; 0 if x<0 CHI (a, x, b) 1 if ab Complex variable functions (page 77): #i square root of -1 ABS (z) absolute value of z SIGN (z) sign of z RE (z) real part of z IM (z) imaginary part of z CONJ (z) complex conjugate of z PHASE (z) phase angle of z Probability functions (page 78): z! z factorial GAMMA (z) gamma of z PERM (z, w) permutations of z things taken w at a time COMB (z, w) combinations of z things taken w at a time Statistical functions (page 79): AVERAGE (z1, ..., zn) arithmetic mean (average) RMS (z1, ..., zn) root mean square VAR (z1, ..., zn) variance STDEV (z1, ..., zn) standard deviation FIT (m) least-squares fit to data matrix m Error functions (page 81): ERF (z) error function ERF (z, w) generalized error function ERFC (z) complementary error function NORMAL (z, m, s) normal distribution function with mean m and standard deviation s Financial functions (page 81): PVAL (i, nper, pmt, fval, time) present value of contract FVAL (i, nper, pmt, pval, time) future value of contract PMT (i, nper, pval, fval, time) periodic payment of contract NPER (i, pmt, pval, fval, time) number of payment periods of contract Calculus functions (page 83): LIM (u, x, a) limit of u as x approaches a from above LIM (u, x, a, 0) limit of u as x approaches a from below DIF (u, x) derivative of u wrt x DIF (u, x, n) nth order derivative of u wrt x TAYLOR (u, x, a, n) nth order Taylor approximation of u about a INT (u, x) antiderivative of u wrt x INT (u, x, a, b) definite integral of u wrt x from a to b SUM (u, n) antidifference of u wrt n SUM (u, n, k, m) definite sum of u as n goes from k to m PRODUCT (u, n) antiquotient of u wrt n PRODUCT (u, n, k, m) definite product of u as n goes from k to m Vector functions (page 94): VECTOR (u, k, m, n, s) a vector of u as k goes from m to n in steps s ELEMENT (v, n) element n of a vector v . w dot product of vectors CROSS (v, w) cross product of two vectors DIMENSION (v) number of elements of a vector OUTER (v, w) outer product of two vectors Matrix functions (page 98): IDENTITY_MATRIX (n) n by n identity matrix ELEMENT (A, j, k) element in row j and column k of a matrix A . B dot product of matrices A` transpose of a matrix (On PC-9801, use Yen char) DET (A) determinant of a square matrix TRACE (A) trace (sum of diagonal) of a square matrix A ^ -1 inverse of a square matrix ROW_REDUCE (A, B) row echelon form of A augmented by B CHARPOLY (A, x) characteristic polynomial of a square matrix EIGENVALUES (A, x) eigenvalues of a square matrix Differential vector calculus (page 104): GRAD (expn) gradient of expn depending on x, y, and z GRAD (expn, v) gradient of expn depending on variables in v GRAD (expn, A) gradient of expn in coordinate system A DIV (v, A) divergence of a vector LAPLACIAN (expn, A) divergence of the gradient of expn CURL (v, A) curl of a vector Integral vector calculus (page 107): POTENTIAL (v) scalar potential of a vector POTENTIAL (v, w) potential of a vector with starting coordinates w VECTOR_POTENTIAL (v) vector potential of a vector JACOBIAN (v, w) Jacobian matrix of partial derivatives COVARIANT_METRIC_TENSOR (J) Covariant metric tensor of Jacobian matrix SQRT_DIAGONAL (G) square roots of the diagonal of a metric tensor Equation operators and functions (page 47): u = v u equals v u /= v u not equal v u < v u less than v u <= v u less than or equal to v u > v u greater than v u >= v u greater than or equal to v SOLVE (u, x) solve u = 0 for x SOLVE (u = v, x) solve u = v for x SOLVE (u = v, x, a, b) solve u = v for x in [a, b] Algebra Window Command Menu To issue a menu option command, press the Space bar until the desired command is highlighted, then press the Enter key. Alternatively, type the letter that is capitalized in the desired command. The following gives the page in the Derive Manual that describes each of the Algebra window's command menu options. 17 Author enter a new expression 22 Build combine expressions Calculus 85 Differentiate differentiate an expression 87 Integrate integrate an expression 83 Limit limit of an expression 91 Product find a closed form product 90 Sum find a closed form sum 86 Taylor find a Taylor approximation Declare 45 Constant declare a constant's value 46 Function declare a function's definition 43 Variable declare a variable's domain 93 Matrix declare a matrix 93 vectoR declare a vector 34 Expand expand an expression 37 Factor factor an expression 11 Help help on 10 Editing line editing commands 71 Functions functions and constants 8 Algebra algebra window commands 55 2D-plot 2D-plot window commands 66 3D-plot 3D-plot window commands 15 State current state of system 11 Return return to Derive 19 Jump highlight an expression 49 soLve solve an equation Manage 37 Branch principal vs real roots 71 Exponential exponential transforms 72 Logarithm logarithmic transforms 34 Ordering variable ordering 41 Substitute substitute in an expression 73 Trigonometry trigonometric transforms Options Color 55 Menu set menu, message, and status line colors 55 Work set expression area colors 53 Display set display mode 12 Execute execute DOS command 29 Input set variable name input mode 10 Mute mute audible error beeps 26 Notation set numeric notation style 24 Precision set arithmetic precision mode 27 Radix set input and output radix bases 55 Plot plot an expression 12 Quit quit Derive 23 Remove remove expressions 19 Simplify simplify an expression Transfer 13 Merge merge expressions from file 14 Clear clear expressions from window 14 Demo simplify expressions from file 13 Load read expressions from file 13 Save write expressions to file Print 14 Printer print expressions to printer 14 File print expressions to file 14 Layout set page size and margins 15 Options set height, range, and character set sTate 16 Load load state from file 16 Save save state in file 22 moVe move expressions Window 64 Close close a window 64 Designate designate window's type 65 Flip flip overlaid windows (= F2 key) 64 Goto go to a given window 64 Next go to next window (= F1 key) 65 Open open a window 64 Previous go to previous window Split split window 63 Horizontal horizontally 63 Vertical vertically 27 approX approximate an expression 2D-plot Window Command Menu To issue a menu option command, press the Space bar until the desired command is highlighted, then press the Enter key. Alternatively, type the letter that is capitalized in the desired command. The following gives the page in the Derive Manual that describes each of the 2D-plot window's command menu options. 58 Algebra switch to an Algebra window 58 Center center window over cross Delete delete from the plot list 59 All all expressions 59 Butlast all but the last expression 59 First the first expression 59 Last the last expression 11 Help help on 10 Editing line editing commands 71 Functions functions and constants 8 Algebra algebra window commands 55 2D-plot 2D-plot window commands 66 3D-plot 3D-plot window commands 15 State current state of system 11 Return return to Derive 56 Move move the cross to coordinates Options 59 Accuracy set plot accuracy Color 60 Plot set plot and axes colors 55 Menu set menu, message, and status line colors 55 Work set plot area background color 53 Display set display mode 12 Execute execute DOS command 10 Mute mute audible error beeps 26 Notation set numeric notation style 24 Precision set arithmetic precision mode 27 Radix set input and output radix bases 62 Type select rectangular or polar plot type 56 Plot plot highlighted expression 12 Quit quit Derive 58 Scale set plot scale 57 Ticks set aspect ratio Window 64 Close close a window 64 Designate designate window's type 65 Flip flip overlaid windows (= F2 key) 64 Goto go to a given window 64 Next go to next window (= F1 key) 65 Open open a window 64 Previous go to previous window Split split window 63 Horizontal horizontally 63 Vertical vertically 57 Zoom zoom plot scale in or out Pressing the F9 function key zooms both axes in. F10 zooms both axes out. On PC compatible computers, pressing the F5 function key switches to the previous display mode as set by an Options Display command. F5 is a fast way to switch between text and graphics display modes. 3D-plot Window Command Menu To issue a menu option command, press the Space bar until the desired command is highlighted, then press the Enter key. Alternatively, type the letter that is capitalized in the desired command. The following gives the page in the Derive Manual that describes each of the 3D-plot window's command menu options. 58 Algebra switch to an Algebra window 69 Center set coordinates of box center 69 Eye set coordinates of viewer's eye 69 Focal set coordinates of focal point 68 Grids set the number of grid panels 68 Hide control display of hidden lines 69 Length set length of sides of box Options 67 Axes control display of axes Color 69 Plot set top, bottom, and axes color 55 Menu set menu, message, and status line colors 55 Work set plot area background color 53 Display set display mode 12 Execute execute DOS command 10 Mute mute audible error beeps 26 Notation set numeric notation style 24 Precision set arithmetic precision mode 27 Radix set input and output radix bases 66 Plot plot highlighted expression 12 Quit quit Derive Window 64 Close close a window 64 Designate designate window's type 65 Flip flip overlaid windows (= F2 key) 64 Goto go to a given window 64 Next go to next window (= F1 key) 65 Open open a window 64 Previous go to previous window Split split window 63 Horizontal horizontally 63 Vertical vertically 69 Zoom zoom box side lengths in or out Current State of System Precision mode *PRECISION* Precision digits *PRECISION-DIGITS* Notation style *NOTATION* Notation digits *NOTATION-DIGITS* Input radix base *INPUT-BASE* Output radix base *OUTPUT-BASE* Input mode *INPUT-MODE* Branch selection *BRANCH* Logarithms *LOG-EXPD* Exponentials *EXP-EXPD* Trig functions *TRIG-EXPD* Trig powers toward *TRIG-SQR* Rows per tick mark *ROWS/TICK* Columns per tick mark *COLS/TICK* 2D plotting accuracy *PLOT-ACCURACY* 2D plot mode *COORDINATE-TYPE* Axes color *AXES-COLOR* Cross color *CROSS-COLOR* 3D top color *TOP-COLOR* 3D bottom color *BOTTOM-COLOR* Frame color *FRAME-COLOR* Option color *OPTION-COLOR* Prompt color *PROMPT-COLOR* Status color *STATUS-COLOR* Menu background color *MENU-BACKGROUND* Border color *BORDER-COLOR* Work color *WORK-COLOR* Work background color *WORK-BACKGROUND* Video mode *VIDEO-MODE* Page length *PAGE-LINES* Page width *PAGE-COLUMNS* Top margin *TOP-MARGIN* Bottom margin *BOTTOM-MARGIN* Left margin *LEFT-MARGIN* Right margin *RIGHT-MARGIN*