Matemáticas#

Introducción #

Math includes both built-in Python functions and the full math module, which is automatically available in VEXcode AIR. These tools allow you to perform everything from basic arithmetic to advanced trigonometry, rounding, and logarithmic operations.

Utilice estas funciones y constantes para calcular posiciones, ángulos, distancias y otros valores numéricos para el controlador de drones VEX AIR. También puede convertir entre grados y radianes, evaluar expresiones y trabajar con valores especiales como infinito y NaN.

Nota: Salvo que se indique explícitamente lo contrario, todos los valores de retorno son números de coma flotante con un formato de cinco decimales. Los valores con más de cinco decimales se redondean, y los valores con menos de cinco decimales se amplían con ceros para que siempre se muestren exactamente cinco decimales.

A continuación se muestra una lista de funciones matemáticas, constantes y utilidades disponibles:

Funciones integradas: herramientas matemáticas comunes incluidas con Python.

abs – Returns the absolute value of a number.
round – Rounds a number to a specified number of decimal places.
min – Returns the smallest of the input values.
max – Returns the largest of the input values.
sum – Adds up all values in an iterable.
divmod – Returns the quotient and remainder as a tuple.
pow – Raises a number to a power, optionally with a modulus.
int – Converts a value to an integer.
float – Converts a value to a floating-point number.

Constants – Predefined values from the math module.

math.pi – The constant π (pi).
math.tau – The constant tau (2π).
math.e – Euler’s number, base of the natural log.
math.inf – Positive infinity.
math.nan – Not a Number (NaN).

Trigonometría – Calcular ángulos y relaciones entre lados.

math.sin – Sine of an angle in radians.
math.cos – Cosine of an angle in radians.
math.tan – Tangent of an angle in radians.
math.asin – Arcsine of a value in radians.
math.acos – Arccosine of a value in radians.
math.atan – Arctangent of a value in radians.
math.atan2 – Arctangent of y/x in radians, considering the quadrant.
math.degrees – Converts radians to degrees.
math.radians – Converts degrees to radians.

Hiperbólicas: funciones trigonométricas avanzadas.

math.sinh – Hyperbolic sine of a value.
math.cosh – Hyperbolic cosine of a value.
math.tanh – Hyperbolic tangent of a value.
math.asinh – Inverse hyperbolic sine.
math.acosh – Inverse hyperbolic cosine.
math.atanh – Inverse hyperbolic tangent.

Redondeo y valor absoluto: ajuste la precisión o la dirección.

math.ceil – Rounds up to the nearest integer.
math.floor – Rounds down to the nearest integer.
math.trunc – Removes the decimal portion.
math.fabs – Returns the absolute value as a float.

Exponentes y logaritmos: cálculos de potencia, raíz y logaritmo.

math.pow – Raises a number to a power.
math.sqrt – Returns the square root.
math.exp – Calculates e to the power of x.
math.log – Natural logarithm (base e).
math.log10 – Base-10 logarithm.
math.log2 – Base-2 logarithm.
math.factorial – Factorial of an integer.
math.expm1 – More accurate result for e^x - 1.

Operaciones de punto flotante: inspeccionar o descomponer valores flotantes.

math.modf – Returns the fractional and integer parts of a float.
math.frexp – Decomposes a number into mantissa and exponent.
math.fmod – Remainder with sign of the dividend.
math.copysign – Returns a value with the sign of another.
math.ldexp – Computes x * (2 ** exp).

Comparación y aproximación: verifique valores con tolerancias o categorías.

math.isfinite – Checks if a number is finite.
math.isinf – Checks if a number is infinite.
math.isnan – Checks if a value is NaN.

Error y Gamma – Funciones matemáticas especiales.

math.gamma – Gamma function (generalized factorial).
math.lgamma – Logarithmic gamma.
math.erf – Error function.
math.erfc – Complementary error function.

Funciones integradas #

Python proporciona varias funciones integradas que le permiten realizar operaciones matemáticas dentro de su proyecto.

abs #

abs returns the absolute value of a number, removing any negative sign.

Usage:
abs(x)

Parámetro	Descripción
`x`	Un número entero o flotante.

# Get the absolute value of -10
abs_result = abs(-10)
controller.screen.print(abs_result)

# abs_result = 10

round #

round returns a rounded a number to a specified number of decimal places as an integer.

Usage:
round(x, ndigits)

Parámetro	Descripción
`x`	Un número entero o flotante.
`ndigits`	Optional. Controls how many decimal places to round to (between 0 and 5). The default is 0. When this parameter is used, `round` returns a float.

# Round 5.7 to the nearest integer
round_int_result = round(5.7)
controller.screen.print(round_int_result)

# round_int_result = 6

# Round 3.14159 to 2 decimal places
round_result = round(3.14159, 2)
controller.screen.print(round_result)

# round_result = 3.14000

min #

min returns the smallest value from multiple arguments or an iterable.

Usage:
min(arg1, arg2, …) or min(sequence)

Parámetro	Descripción
`arg1`, `arg2`, …	Los números para comparar.
`sequence`	Una lista, tupla u otra secuencia que contiene números.

# Get the smallest number from 3, 7, and 1
min_result = min(3, 7, 1)
controller.screen.print(min_result)

# min_result = 1

# Get the smallest value from a list
min_list_result = min([10, 4, 25, 1])
controller.screen.print(min_list_result)

# min_list_result = 1

max #

max returns the largest value from multiple arguments or an iterable.

Usage:
max(arg1, arg2, …) or max(sequence)

Parámetro	Descripción
`arg1`, `arg2`, …	Los números para comparar.
`sequence`	Una lista, tupla u otra secuencia que contiene números.

# Get the largest number from 3, 7, and 1
max_result = max(3, 7, 1)
controller.screen.print(max_result)

# max_result = 7

# Get the largest value from a list
max_list_result = max([10, 4, 25, 1])
controller.screen.print(max_list_result)

# max_list_result = 25

sum #

sum adds up all values in an iterable, with an optional starting value.

Usage:
sum(sequence, start)

Parámetro	Descripción
`sequence`	Una lista, tupla u otra secuencia que contiene números.
`start`	Opcional. Un valor para añadir a la suma. El valor predeterminado es 0.

# Calculate the sum of a list of numbers
sum_result = sum([1, 2, 3, 4, 5])
controller.screen.print(sum_result)

# sum_result = 15

# Calculate the sum of a list with a starting value of 10
sum_with_start = sum([1, 2, 3], 10)
controller.screen.print(sum_with_start)

# sum_with_start = 16

divmod #

divmod returns a tuple containing the quotient and remainder of a division operation.

Usage:
divmod(a, b)

Parámetro	Descripción
`a`	El dividendo.
`b`	El divisor.

# Perform integer division and remainder of 10 / 3
divmod_result = divmod(10, 3)
controller.screen.print(divmod_result)

# divmod_result = (3, 1)

pow #

pow returns a number raised to a power and optionally performs a modulus operation as an integer.

Usage:
pow(x, y, mod)

Parámetro	Descripción
`x`	El número base.
`y`	El exponente.
`mod`	Optional. A modulus value. If provided, returns `(x ** y) % mod`.

# Calculate 2 raised to the power of 3
pow_result = pow(2, 3)
controller.screen.print(pow_result)

# pow_result = 8

# Calculate (5 ** 3) % 7
pow_mod_result = pow(5, 3, 7)
controller.screen.print(pow_mod_result)

# pow_mod_result = 6

int #

>int converts a number or string into an integer. It also supports base conversion when converting from a string.

Usage:
int(x, base)

Parámetro	Descripción
`x`	Un número, una cadena u otro objeto para convertir.
`base`	Opcional. La base numérica que se usará para la conversión. El valor predeterminado es 10.

# Convert a float to an integer to get rid of decimals
price = 19.99
price_int = int(price)
controller.screen.print(f"{price_int} coins")

# Output: 19 coins

# Convert a string into an integer to use in calculations
user_input = "55"
user_number = int(user_input)
controller.screen.print(user_number * 2)

# Output: 110

float #

float converts a number or string into a floating-point number.

Usage:
float(x)

Parámetro	Descripción
`x`	Un número, una cadena u otro objeto para convertir.

# Convert division result to a float
num_apples = 6
num_people = 2
apples_per_person = float(num_apples) / num_people
controller.screen.print(apples_per_person)

# Output: 3.00000

# Convert a string into a float to use in calculations
user_input = "23.4"
user_number = float(user_input)
controller.screen.print(user_number * 3)

# Output: 70.20000

Módulo de matemáticas #

The math module in MicroPython provides additional methods for performing common mathematical calculations. These methods include trigonometric, logarithmic, and other numerical operations.

The math module is imported by default in VEXcode.

Constants #

Las constantes son valores predefinidos que permanecen fijos durante un proyecto. Pueden utilizarse en cálculos sin necesidad de definirlas ni asignarlas.

pi #

pi gives the mathematical constant π, the ratio of a circle’s circumference to its diameter.

Usage:
math.pi

# Calculate the area of a circle with radius 5 using pi
circle_area = math.pi * 5 * 5
controller.screen.print(circle_area)

# circle_area = 78.53982

tau #

tau gives the value of 2π.

Usage:
math.tau

# Calculate the circumference of a circle with radius
circumference = math.tau * 5
controller.screen.print(circumference)

# circumference = 31.41593

mi #

e gives the base of the natural logarithm.

Usage:
math.e

# Calculate e raised to the power of 2
e_power = math.pow(math.e, 2)
controller.screen.print(e_power)

# e_power = 7.38906

información #

inf gives positive infinity as a float.

Usage:
math.inf

# Check if infinity is infinite
inf_value = math.inf

if math.isinf(inf_value):
    controller.screen.print("Infinity")

# Prints "Infinity"

yaya #

nan represents a special float for “Not a Number” (NaN).

Usage:
math.nan

# Check if nan is Not a Number
nan_value = math.nan

if math.isnan(nan_value):
    controller.screen.print("Not a Number")

# Prints "Not a Number"

Trigonometry #

pecado #

sin calculates the sine of an angle in radians and returns a float.

Usage:
math.sin(x)

Parámetro	Descripción
`x`	Un flotante o entero que representa un ángulo en radianes.

# Calculate the sine of 30 degrees in radians
sine_result = math.sin(math.radians(30))
controller.screen.print(sine_result)

# sine_result = 0.50000

porque #

cos calculates the cosine of an angle in radians and returns a float.

Usage:
math.cos(x)

Parámetro	Descripción
`x`	Un flotante o entero que representa un ángulo en radianes.

# Calculate the cosine of 60 degrees in radians
cosine_result = math.cos(math.radians(60))
controller.screen.print(cosine_result)

# cosine_result = 0.50000

broncearse #

tan calculates the tangent of an angle in radians and returns a float.

Usage:
math.tan(x)

Parámetro	Descripción
`x`	Un flotante o entero que representa un ángulo en radianes.

# Calculate the tangent of 45 degrees in radians
tangent_result = math.tan(math.radians(45))
controller.screen.print(tangent_result)

# tangent_result = 1.00000

asiático #

asin calculates the inverse sine (arc sine) of a number and returns a float representing the angle in radians.

Usage:
math.asin(x)

Parámetro	Descripción
`x`	Un número flotante o entero entre -1 y 1.

# Calculate the arc sine of 0.5 in radians
arc_sine_result = math.asin(0.5)
controller.screen.print(arc_sine_result)

# arc_sine_result = 0.52360

acos #

acos calculates the inverse cosine (arc cosine) of a number and returns a float representing the angle in radians.

Usage:
>math.acos(x)

Parámetro	Descripción
`x`	Un número flotante o entero entre -1 y 1.

# Calculate the arc cosine of 0.5 in radians
arc_cosine_result = math.acos(0.5)
controller.screen.print(arc_cosine_result)

# arc_cosine_result = 1.04720

Atán #

atan calculates the inverse tangent (arc tangent) of a number and returns a float representing the angle in radians.

Usage:
math.atan(x)

Parámetro	Descripción
`x`	Un flotante o entero.

# Calculate the arc tangent of 1 in radians
arc_tangent_result = math.atan(1)
controller.screen.print(arc_tangent_result)

# arc_tangent_result = 0.78540

atan2 #

atan2 calculates the principal value of the inverse tangent of y/x and returns a float representing the angle in radians.

Usage:
math.atan2(y, x)

Parámetro	Descripción
`y`	Un flotante o entero que representa la coordenada y.
`x`	Un flotante o entero que representa la coordenada x.

# Calculate the inverse tangent of (4, 3) in radians
atan2_result = math.atan2(3, 4)
controller.screen.print(atan2_result)

# atan2_result = 0.64350

grados #

degrees converts an angle from radians to degrees.

Usage:
math.degrees(x)

Parámetro	Descripción
`x`	Un flotante o entero que representa un ángulo en radianes.

# Convert pi radians to degrees
degrees_result = math.degrees(math.pi)
controller.screen.print(degrees_result)

# degrees_result = 180.00000

radianes #

radians converts an angle from degrees to radians.

Usage:
math.radians(x)

Parámetro	Descripción
`x`	Un flotante o entero que representa un ángulo en grados.

# Convert 180 degrees to radians
radians_result = math.radians(180)
controller.screen.print(radians_result)

# radians_result = 3.14159

Hyperbolics #

Sinh #

sinh calculates the hyperbolic sine of x.

Usage:
math.sinh(x)

Parámetro	Descripción
`x`	Un flotante o entero que representa el valor de entrada.

# Calculate the hyperbolic sine of 1
sinh_result = math.sinh(1)
controller.screen.print(sinh_result)

# sinh_result = 1.7520

aporrear #

cosh calculates the hyperbolic cosine of x.

Usage:
math.cosh(x)

Parámetro	Descripción
`x`	Un flotante o entero que representa el valor de entrada.

# Calculate the hyperbolic cosine of 1
cosh_result = math.cosh(1)
controller.screen.print(cosh_result)

# cosh_result = 1.54308

tanh #

tanh calculates the hyperbolic tangent of x.

Usage:
math.tanh(x)

Parámetro	Descripción
`x`	Un flotante o entero que representa el valor de entrada.

# Calculate the hyperbolic tangent of 1
tanh_result = math.tanh(1)
controller.screen.print(tanh_result)

# tanh_result = 0.76159

asiático #

asinh calculates the inverse hyperbolic sine of x.

Usage:
math.asinh(x)

Parámetro	Descripción
`x`	Un flotante o entero que representa el valor de entrada.

# Calculate the inverse hyperbolic sine of 1
asinh_result = math.asinh(1)
controller.screen.print(asinh_result)

# asinh_result = 0.88137

acosh #

acosh calculates the inverse hyperbolic cosine of x.

Usage:
math.acosh(x)

Parámetro	Descripción
`x`	Un flotante o entero mayor o igual a 1.

# Calculate the inverse hyperbolic cosine of 2
acosh_result = math.acosh(2)
controller.screen.print(acosh_result)

# acosh_result = 1.31696

Atanh #

atanh calculates the inverse hyperbolic tangent of x.

Usage:
math.atanh(x)

Parámetro	Descripción
`x`	Un flotante entre -1 y 1 (exclusivo).

# Calculate the inverse hyperbolic tangent of 0.5
atanh_result = math.atanh(0.5)
controller.screen.print(atanh_result)

# atanh_result = 0.54931

Rounding & Absolute Values #

fortificar techo #

ceil rounds a number up to the nearest integer.

Usage:
math.ceil(x)

Parámetro	Descripción
`x`	Un número flotante o entero que se redondeará hacia arriba.

# Round 3.7 up to the nearest integer
ceil_result = math.ceil(3.7)
controller.screen.print(ceil_result)

# ceil_result = 4

piso #

floor rounds a number down to the nearest integer.

Usage:
math.floor(x)

Parámetro	Descripción
`x`	Un número flotante o entero que se redondeará hacia abajo.

# Round 3.7 down to the nearest integer
floor_result = math.floor(3.7)
controller.screen.print(floor_result)

# floor_result = 3

tronco #

trunc removes the decimal part of a number without rounding.

Usage:
math.trunc(x)

Parámetro	Descripción
`x`	Un flotador que debe truncarse.

# Remove the decimal part of 3.7
trunc_result = math.trunc(3.7)
controller.screen.print(trunc_result)

# trunc_result = 3

fábricas #

fabs returns the absolute value of a number as a float.

Usage:
math.fabs(x)

Parámetro	Descripción
`x`	Un flotante o entero.

# Get the absolute value of -3.7
fabs_result = math.fabs(-3.7)
controller.screen.print(fabs_result)

# fabs_result = 3.70000

Exponents & Logarithms #

poder #

pow raises x to the power of y (x^y) and returns a float.

Usage:
math.pow(x, y)

Parámetro	Descripción
`x`	Una base de número flotante o entero.
`y`	Un exponente flotante o entero.

# Calculate 2 raised to the power of 3
power_result = math.pow(2, 3)
controller.screen.print(power_result)

# power_result = 8.00000

raíz cuadrada #

sqrt calculates the square root of a number and returns a float.

Usage:
math.sqrt(x)

Parámetro	Descripción
`x`	Un número entero o flotante no negativo.

# Calculate the square root of 16
sqrt_result = math.sqrt(16)
controller.screen.print(sqrt_result)

# sqrt_result = 4.00000

exp #

exp returns e raised to the power of x (e^x) and as a float.

Usage:
math.exp(x)

Parámetro	Descripción
`x`	Un flotante o entero.

# Calculate e raised to the power of 1
exp_result = math.exp(1)
controller.screen.print(exp_result)

# exp_result = 2.71828

registro #

log calculates the natural logarithm of a number and returns a float.

Usage:
math.log(x)

Parámetro	Descripción
`x`	Un número entero o flotante positivo.

# Calculate the natural logarithm (base e) of 7.389056
log_result = math.log(7.389056)
controller.screen.print(log_result)

# log_result = 2.00000

registro10 #

log10 calculates the base-10 logarithm of a number and returns a float.

Usage:
math.log10(x)

Parámetro	Descripción
`x`	Un número entero o flotante positivo.

# Calculate the base-10 logarithm of 1000
log10_result = math.log10(1000)
controller.screen.print(log10_result)

# log10_result = 3.00000

registro2 #

log2 calculates the base-2 logarithm of a number and returns a float, even when x is a power of 2.

Usage:
math.log2(x)

Parámetro	Descripción
`x`	Un número entero o flotante positivo.

# Calculate the base-2 logarithm of 8
log2_result = math.log2(8)
controller.screen.print(log2_result)

# log2_result = 3.00000

factorial #

factorial returns the factorial of an integer x, which is the product of all positive integers up to x.

Usage:
math.factorial(x)

Parámetro	Descripción
`x`	Un entero no negativo.

# Calculate 5 factorial (5!)
factorial_result = math.factorial(5)
controller.screen.print(factorial_result)

# factorial_result = 120

expm1 #

expm1 calculates e^x - 1, which is more accurate for small x.

Usage:
math.expm1(x)

Parámetro	Descripción
`x`	El valor del exponente.

# Compute expm1(1) (e^1 - 1)
expm1_result = math.expm1(1)
controller.screen.print(expm1_result)

# expm1_result = 1.71828

Floating Point Operations #

modf #

modf decomposes a number into its fractional and integer parts and returns a tuple (fractional part, integer part), both as floats.

Usage:
math.modf(x)

Parámetro	Descripción
`x`	Un flotante o entero para descomponer.

# Decompose 3.14159 into fractional and integer parts
fractional_part, integer_part = math.modf(3.14159)
controller.screen.print(fractional_part)
controller.screen.next_row()
controller.screen.print(integer_part)

# fractional_part = 0.14159
# integer_part = 3.00000

frexp #

frexp decomposes a number into its mantissa and exponent and returns a tuple (mantissa, exponent), where the mantissa is a float and the exponent is an integer.

Usage:
math.frexp(x)

Parámetro	Descripción
`x`	Un flotante o entero para descomponer.

# Decompose 16 into its mantissa and exponent
mantissa, exponent = math.frexp(16)
controller.screen.print(mantissa)
controller.screen.next_row()
controller.screen.print(exponent)

# mantissa = 0.50000
# exponent = 5

fmod #

fmod returns the remainder of division while keeping the sign of the dividend (x).

Usage:
math.fmod(x, y)

Parámetro	Descripción
`x`	El dividendo.
`y`	El divisor.

# Calculate remainder of 10 / 3
# that preserves the sign of 10
fmod_result = math.fmod(10, 3)
controller.screen.print(fmod_result)

# fmod_result = 1.00000

firma de derechos de autor #

copysign returns x with the sign of y.

Usage:
math.copysign(x, y)

Parámetro	Descripción
`x`	El valor a modificar.
`y`	El valor cuyo signo se copiará.

# Return -10 with the sign of 3 (positive)
copysign_result = math.copysign(-10, 3)
controller.screen.print(copysign_result)

# copysign_result = 10.00000

ldexp #

ldexp computes x * (2 ** exp), which is equivalent to x * 2^exp.

Usage:
math.ldexp(x, exp)

Parámetro	Descripción
`x`	El valor base.
`exp`	El exponente.

# Compute 3 * (2 ** 4)
ldexp_result = math.ldexp(3, 4)
controller.screen.print(ldexp_result)

# ldexp_result = 48.00000

Comparison & Approximation #

es finito #

isfinite checks if a number is finite. This method returns a Boolean value:

True - The number is finite.
False - The number is infinite.

Usage:
math.isfinite(x)

Parámetro	Descripción
`x`	Un flotante o entero para comprobar.

# Check if 42 is a finite number (returns True)
is_finite_true = math.isfinite(42)
controller.screen.print(is_finite_true)

# is_finite_true = True

# Check if infinity is a finite number (returns False)
is_finite_false = math.isfinite(math.inf)
controller.screen.print(is_finite_false)

# is_finite_false = False

es inf #

isinf checks if a number is infinite. This method returns a Boolean value:

True - The number is infinite.
False - The number is finite.

Usage:
math.isinf(x)

Parámetro	Descripción
`x`	Un flotante o entero para comprobar.

# Check if infinity is an infinite number (returns True)
is_inf_true = math.isinf(math.inf)
controller.screen.print(is_inf_true)

# is_inf_true = True

# Check if 42 is an infinite number (returns False)
is_inf_false = math.isinf(42)
controller.screen.print(is_inf_false)

# is_inf_false = False

Isnan #

isnan checks if a number is NaN (Not a Number). This method returns a Boolean value:

True - The number is NaN.
False - The number is a valid number.

Usage:
math.isnan(x)

Parámetro	Descripción
`x`	Un flotante o entero para comprobar.

# Check if NaN (Not a Number) is NaN (returns True)
is_nan_true = math.isnan(math.nan)
controller.screen.print(is_nan_true)

# is_nan_true = True

# Check if 42 is NaN (returns False)
is_nan_false = math.isnan(42)
controller.screen.print(is_nan_false)

# is_nan_false = False

Error and Gamma Calculations #

gama #

gamma computes the gamma function of x, which generalizes the factorial function for real and complex numbers. For an integer n, gamma(n) = (n-1)!.

Usage:
math.gamma(x)

Parámetro	Descripción
`x`	Un número entero o flotante positivo.

# Calculate the gamma function of 5 (equivalent to 4!)
gamma_result = math.gamma(5)
controller.screen.print(gamma_result)

# gamma_result = 24.00000

lgamma #

lgamma computes the natural logarithm of the gamma function.

Usage:
math.lgamma(x)

Parámetro	Descripción
`x`	Un número entero o flotante positivo.

# Calculate the natural logarithm of the
# gamma function of 5
lgamma_result = math.lgamma(5)
controller.screen.print(lgamma_result)

# lgamma_result = 3.17805

erf #

erf computes the error function of x.

Usage:
math.erf(x)

Parámetro	Descripción
`x`	Un flotante o entero que representa el valor de entrada.

# Calculate the error function of 1
erf_result = math.erf(1)
controller.screen.print(erf_result)

# erf_result = 0.84270

erfc #

erfc computes the complementary error function of x, which is defined as 1 - erf(x).

Usage:
math.erfc(x)

Parámetro	Descripción
`x`	Un flotante o entero que representa el valor de entrada.

# Calculate the complementary error function of 1
erfc_result = math.erfc(1)
controller.screen.print(erfc_result)

# erfc_result = 0.15730