Dystlab uses its own math engine, MathSIV©, in its digital products. This high-tech tool allows you to perform mathematical calculations, solve systems of equations, convert expressions into symbolic (analytical) form, perform numerical and symbolic differentiation and integration, and more. MathSIV supports real numbers ("-2.5", "4.6e8", "Pi"), complex numbers ("2+3.2I"), one-, two-, and three-dimensional vectors and matrices ("M=[1 2 3]"), logical data types ("if{x<1}(a b)"), and physical quantities with arbitrary units (A=2.5 mm^2).
Note: In some browsers, certain symbols in this list may be replaced by squares or other symbols (example: Y₁). However, you can still copy such operators or functions and use them in your project — they should be displayed correctly in TechEditor and other programs.
Operators | Оператори
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!
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‖ ‖
*
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&
#
•
•{ }
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^
←
→
↑
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↔
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∂
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<
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√
∫
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≥
Directives and common functions | Директиви та загальні фукнції
DERIVATIVE{x}(expression)
Returns the symbolic derivative of "expression" with respect to the variable "x".
- x — variable name;
- expression — valid math expression.
Examples:
DERIVATIVE{x}(sin(x^3)) = cos(x^3)*3*x^2
EVALUATE{EXPLICIT}(expression)
Returns the symbolic derivative or integral of "expression".
- EXPLICIT — reserved word;
- expression — valid math expression.
Examples:
EVALUATE{EXPLICIT}(∫sin(x)^2∂x) = -((sin(x)*cos(x))/2)+(1/2)*x
EVALUATE{SIMPLIFY}(expression)
Simplifies "expression" and returns its symbolic representation.
- SIMPLIFY — reserved word;
- expression — valid math expression.
Examples:
EVALUATE{SIMPLIFY}(A*(x^2+1-1/3)-4*x/B/2) = A*(x^2+2/3)-2*x/B
FOR{i=N:M}(body)
FOR loop directive.
- i — loop variable (must be initialized first);
- N — the initial value of the loop variable “i”;
- M — the final value of the loop variable “i”;
- body — valid math statement.
Examples:
i=0
FOR{i=0:10}(A[i]=i*2)
FOR{i=-3:100}(A[i]=if{i≤50}(0 1))
FOR{i=0:#M-1}(IF{X[i]≡4}(M[i]=4 M[i]=-2))
if{}()
IF{condition}(A B)
INTEGRAL{x}(expression)
Returns the symbolic integral of "expression" with respect to the variable "x".
- x — variable name;
- expression — valid math expression.
Examples:
INTEGRAL{x}(e^x*x^2) = x^2*e^x-2*(x*e^x-e^x)