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diff --git a/src/main/java/org/apache/commons/math3/ode/FirstOrderFieldIntegrator.java b/src/main/java/org/apache/commons/math3/ode/FirstOrderFieldIntegrator.java
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+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math3.ode;
+
+import org.apache.commons.math3.RealFieldElement;
+import org.apache.commons.math3.analysis.solvers.BracketedRealFieldUnivariateSolver;
+import org.apache.commons.math3.exception.MaxCountExceededException;
+import org.apache.commons.math3.exception.NoBracketingException;
+import org.apache.commons.math3.exception.NumberIsTooSmallException;
+import org.apache.commons.math3.ode.events.FieldEventHandler;
+import org.apache.commons.math3.ode.sampling.FieldStepHandler;
+
+import java.util.Collection;
+
+/**
+ * This interface represents a first order integrator for differential equations.
+ *
+ * <p>The classes which are devoted to solve first order differential equations should implement
+ * this interface. The problems which can be handled should implement the {@link
+ * FirstOrderDifferentialEquations} interface.
+ *
+ * @see FirstOrderFieldDifferentialEquations
+ * @param <T> the type of the field elements
+ * @since 3.6
+ */
+public interface FirstOrderFieldIntegrator<T extends RealFieldElement<T>> {
+
+    /**
+     * Get the name of the method.
+     *
+     * @return name of the method
+     */
+    String getName();
+
+    /**
+     * Add a step handler to this integrator.
+     *
+     * <p>The handler will be called by the integrator for each accepted step.
+     *
+     * @param handler handler for the accepted steps
+     * @see #getStepHandlers()
+     * @see #clearStepHandlers()
+     */
+    void addStepHandler(FieldStepHandler<T> handler);
+
+    /**
+     * Get all the step handlers that have been added to the integrator.
+     *
+     * @return an unmodifiable collection of the added events handlers
+     * @see #addStepHandler(FieldStepHandler)
+     * @see #clearStepHandlers()
+     */
+    Collection<FieldStepHandler<T>> getStepHandlers();
+
+    /**
+     * Remove all the step handlers that have been added to the integrator.
+     *
+     * @see #addStepHandler(FieldStepHandler)
+     * @see #getStepHandlers()
+     */
+    void clearStepHandlers();
+
+    /**
+     * Add an event handler to the integrator.
+     *
+     * <p>The default solver is a 5<sup>th</sup> order {@link
+     * org.apache.commons.math3.analysis.solvers.FieldBracketingNthOrderBrentSolver}.
+     *
+     * @param handler event handler
+     * @param maxCheckInterval maximal time interval between switching function checks (this
+     *     interval prevents missing sign changes in case the integration steps becomes very large)
+     * @param convergence convergence threshold in the event time search
+     * @param maxIterationCount upper limit of the iteration count in the event time search events.
+     * @see #addEventHandler(FieldEventHandler, double, double, int,
+     *     org.apache.commons.math3.analysis.solvers.BracketedRealFieldUnivariateSolver)
+     * @see #getEventHandlers()
+     * @see #clearEventHandlers()
+     */
+    void addEventHandler(
+            FieldEventHandler<T> handler,
+            double maxCheckInterval,
+            double convergence,
+            int maxIterationCount);
+
+    /**
+     * Add an event handler to the integrator.
+     *
+     * @param handler event handler
+     * @param maxCheckInterval maximal time interval between switching function checks (this
+     *     interval prevents missing sign changes in case the integration steps becomes very large)
+     * @param convergence convergence threshold in the event time search
+     * @param maxIterationCount upper limit of the iteration count in the event time search events.
+     * @param solver solver to use to locate the event
+     * @see #addEventHandler(FieldEventHandler, double, double, int)
+     * @see #getEventHandlers()
+     * @see #clearEventHandlers()
+     */
+    void addEventHandler(
+            FieldEventHandler<T> handler,
+            double maxCheckInterval,
+            double convergence,
+            int maxIterationCount,
+            BracketedRealFieldUnivariateSolver<T> solver);
+
+    /**
+     * Get all the event handlers that have been added to the integrator.
+     *
+     * @return an unmodifiable collection of the added events handlers
+     * @see #addEventHandler(FieldEventHandler, double, double, int)
+     * @see #clearEventHandlers()
+     */
+    Collection<FieldEventHandler<T>> getEventHandlers();
+
+    /**
+     * Remove all the event handlers that have been added to the integrator.
+     *
+     * @see #addEventHandler(FieldEventHandler, double, double, int)
+     * @see #getEventHandlers()
+     */
+    void clearEventHandlers();
+
+    /**
+     * Get the current value of the step start time t<sub>i</sub>.
+     *
+     * <p>This method can be called during integration (typically by the object implementing the
+     * {@link FirstOrderDifferentialEquations differential equations} problem) if the value of the
+     * current step that is attempted is needed.
+     *
+     * <p>The result is undefined if the method is called outside of calls to <code>integrate</code>
+     * .
+     *
+     * @return current value of the state at step start time t<sub>i</sub>
+     */
+    FieldODEStateAndDerivative<T> getCurrentStepStart();
+
+    /**
+     * Get the current signed value of the integration stepsize.
+     *
+     * <p>This method can be called during integration (typically by the object implementing the
+     * {@link FirstOrderDifferentialEquations differential equations} problem) if the signed value
+     * of the current stepsize that is tried is needed.
+     *
+     * <p>The result is undefined if the method is called outside of calls to <code>integrate</code>
+     * .
+     *
+     * @return current signed value of the stepsize
+     */
+    T getCurrentSignedStepsize();
+
+    /**
+     * Set the maximal number of differential equations function evaluations.
+     *
+     * <p>The purpose of this method is to avoid infinite loops which can occur for example when
+     * stringent error constraints are set or when lots of discrete events are triggered, thus
+     * leading to many rejected steps.
+     *
+     * @param maxEvaluations maximal number of function evaluations (negative values are silently
+     *     converted to maximal integer value, thus representing almost unlimited evaluations)
+     */
+    void setMaxEvaluations(int maxEvaluations);
+
+    /**
+     * Get the maximal number of functions evaluations.
+     *
+     * @return maximal number of functions evaluations
+     */
+    int getMaxEvaluations();
+
+    /**
+     * Get the number of evaluations of the differential equations function.
+     *
+     * <p>The number of evaluations corresponds to the last call to the <code>integrate</code>
+     * method. It is 0 if the method has not been called yet.
+     *
+     * @return number of evaluations of the differential equations function
+     */
+    int getEvaluations();
+
+    /**
+     * Integrate the differential equations up to the given time.
+     *
+     * <p>This method solves an Initial Value Problem (IVP).
+     *
+     * <p>Since this method stores some internal state variables made available in its public
+     * interface during integration ({@link #getCurrentSignedStepsize()}), it is <em>not</em>
+     * thread-safe.
+     *
+     * @param equations differential equations to integrate
+     * @param initialState initial state (time, primary and secondary state vectors)
+     * @param finalTime target time for the integration (can be set to a value smaller than {@code
+     *     t0} for backward integration)
+     * @return final state, its time will be the same as {@code finalTime} if integration reached
+     *     its target, but may be different if some {@link
+     *     org.apache.commons.math3.ode.events.FieldEventHandler} stops it at some point.
+     * @exception NumberIsTooSmallException if integration step is too small
+     * @exception MaxCountExceededException if the number of functions evaluations is exceeded
+     * @exception NoBracketingException if the location of an event cannot be bracketed
+     */
+    FieldODEStateAndDerivative<T> integrate(
+            FieldExpandableODE<T> equations, FieldODEState<T> initialState, T finalTime)
+            throws NumberIsTooSmallException, MaxCountExceededException, NoBracketingException;
+}