diff --git a/kmath-ast/src/jvmTest/kotlin/scietifik/kmath/ast/asm/TestAsmAlgebras.kt b/kmath-ast/src/jvmTest/kotlin/scietifik/kmath/ast/asm/TestAsmAlgebras.kt
new file mode 100644
index 000000000..07f895c40
--- /dev/null
+++ b/kmath-ast/src/jvmTest/kotlin/scietifik/kmath/ast/asm/TestAsmAlgebras.kt
@@ -0,0 +1,75 @@
+package scietifik.kmath.ast.asm
+
+import scientifik.kmath.asm.asmField
+import scientifik.kmath.asm.asmRing
+import scientifik.kmath.asm.asmSpace
+import scientifik.kmath.expressions.invoke
+import scientifik.kmath.operations.ByteRing
+import scientifik.kmath.operations.RealField
+import kotlin.test.Test
+import kotlin.test.assertEquals
+
+class TestAsmAlgebras {
+    @Test
+    fun space() {
+        val res = ByteRing.asmSpace {
+            binaryOperation(
+                "+",
+
+                unaryOperation(
+                    "+",
+                    3.toByte() - (2.toByte() + (multiply(
+                        add(const(1), const(1)),
+                        2
+                    ) + 1.toByte()) * 3.toByte() - 1.toByte())
+                ),
+
+                number(1)
+            ) + variable("x") + zero
+        }("x" to 2.toByte())
+
+        assertEquals(16, res)
+    }
+
+    @Test
+    fun ring() {
+        val res = ByteRing.asmRing {
+            binaryOperation(
+                "+",
+
+                unaryOperation(
+                    "+",
+                    (3.toByte() - (2.toByte() + (multiply(
+                        add(const(1), const(1)),
+                        2
+                    ) + 1.toByte()))) * 3.0 - 1.toByte()
+                ),
+
+                number(1)
+            ) * const(2)
+        }()
+
+        assertEquals(24, res)
+    }
+
+    @Test
+    fun field() {
+        val res = RealField.asmField {
+            divide(binaryOperation(
+                "+",
+
+                unaryOperation(
+                    "+",
+                    (3.0 - (2.0 + (multiply(
+                        add(const(1.0), const(1.0)),
+                        2
+                    ) + 1.0))) * 3 - 1.0
+                ),
+
+                number(1)
+            ) / 2, const(2.0)) * one
+        }()
+
+        assertEquals(3.0, res)
+    }
+}
diff --git a/kmath-ast/src/jvmTest/kotlin/scietifik/kmath/ast/asm/TestAsmExpressions.kt b/kmath-ast/src/jvmTest/kotlin/scietifik/kmath/ast/asm/TestAsmExpressions.kt
new file mode 100644
index 000000000..2839b8a25
--- /dev/null
+++ b/kmath-ast/src/jvmTest/kotlin/scietifik/kmath/ast/asm/TestAsmExpressions.kt
@@ -0,0 +1,21 @@
+package scietifik.kmath.ast.asm
+
+import scientifik.kmath.asm.asmField
+import scientifik.kmath.expressions.invoke
+import scientifik.kmath.operations.RealField
+import kotlin.test.Test
+import kotlin.test.assertEquals
+
+class TestAsmExpressions {
+    @Test
+    fun testUnaryOperationInvocation() {
+        val res = RealField.asmField { unaryOperation("+", variable("x")) }("x" to 2.0)
+        assertEquals(2.0, res)
+    }
+
+    @Test
+    fun testConstProductInvocation() {
+        val res = RealField.asmField { variable("x") * 2 }("x" to 2.0)
+        assertEquals(4.0, res)
+    }
+}