Modulo Function (Remainder)

Function Form

$$y=\text{Mod}(x,d)=x\mathrm{mod}d$$

Additional Variables

$q\in \mathbb{Z}$: Integer part of $\frac{x}{d}$.

$r\in [0,|d|)$: Remainder part of $\frac{x}{d}$.

Derived Symbol

$$y=r$$

Mathematical Model

$$\begin{array}{rl}\text{s.t.}& x=d\cdot q+r\end{array}$$

Code Example

kotlin

import kotlinx.coroutines.*
import fuookami.ospf.kotlin.utils.math.*
import fuookami.ospf.kotlin.core.frontend.variable.*
import fuookami.ospf.kotlin.core.frontend.expression.polynomial.*
import fuookami.ospf.kotlin.core.frontend.expression.symbol.linear_function.*
import fuookami.ospf.kotlin.core.frontend.inequality.*
import fuookami.ospf.kotlin.core.frontend.model.mechanism.*
import fuookami.ospf.kotlin.core.backend.plugins.scip.*

val x = RealVar("x")
x.range.eq(Flt64.three)
val mod = ModFunction(x, Flt64(0.7), name = "mod")

val model = LinearMetaModel()
model.add(x)
model.add(mod)
model.minimize(mod)

val solver = ScipLinearSolver()
val result = runBlocking { solver(model) }
assert(result.value!!.obj eq Flt64(0.2))

Complete Implementation Reference:

• Kotlin

Complete Example Reference:

• Kotlin