About symbolic calculations in calculla
Short view of symbolic math support in calculla.

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About symbolic calculations in calculla

li]To calculate the results you are looking for, we generally need one or more numbers from you.
  • For example, our disk area calculator will tell us that a disk area with a radius of 1 is π\pi or about 3.14. But did you know that using Calculla you can also check that the area of ​​the disk with radius 2ππ\dfrac{2\sqrt{\pi}}{\pi} is exactly four (4)?
  • Calculla is great at numbers, but an increasing proportion of our calculators also works with symbols such as a, b, r or α\alpha, β\beta, γ\gamma , π\pi etc.
  • Calculations which instead of numbers (e.g. 1, 2, 12.5) operate on mathematical symbols (e.g. a, b, x) is called often symbolic calculations.
  • Using symbolic calculations (instead of numeric ones):
    • is closer to the way how people work e.g. doing transformations on a paper sheet or writing chalk on a blackboard,
    • enables better tracking of individual steps such as fractions cancelling, applying short multiplication formulas or using one of the trigonometric reduction patterns,
    • often allows to keep the calculation context that would be lost in the case of calculations involving numbers,
    • allows to find general solutions e.g. to determine the roots of a quadratic equation with a parameter. Below is an example equation with the parameter t whose solution in the traditional way (from the point of view of computer software) would not be possible until we determined the numerical value of the parameter:
      tx2+2x+3=0tx ^ 2 + 2x + 3 = 0
    • allows to avoid unnecessary rounding e.g. during operations on fractions,
    • in the case of calculations related to the natural or engineering sciences, it allows to preserve physical sense or even to find new general relationships between quantities which would not be possible if we obtained a single number as a result, e.g. 2.1564363424.
  • Software that performs symbolic calculations is sometimes referred as CAS derived from the phrase Computer Algebra System. We can therefore say that Calculla is increasingly becoming one of the CAS systems.

How to use symbolic calculations in our calculators?

  • For calculators that support symbolic calculations, you can specifysymbolic expressionsin addition to numbers.
  • Symbolic expressions may contain:
    • single numbers in the decimal system, e.g. 1, 4, 3.14. In this case, they do not differ from the decimal numbers,
    • single letter symbols (parameters) e.g. a, b, c,
    • popular mathematical constants, e.g. pi means pi number,
    • arithmetic operations containing numbers or symbols:
      • addition e.g. a + b (sum of symbols a and b),
      • multiplication e.g. 2 * x (product of the number two and the symbol x),
      • division or fractions e.g. pi/a (quotient of the number π\pi and the symbol a),
      • exponentiation e.g. r^2 (symbol r squared),
      • square root e.g. sqrt(a + b) (root from the sum of the symbols a and b),
      • popular mathematical functions e.g. sin(x) (sine from the symbol x), cos(pi/2) (cosine of the number π2)\frac{\pi}{2}), exp(-r^2) (value of the exponential function from minus r square) etc.
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