diff --git a/pysindy/feature_library/identity_library.py b/pysindy/feature_library/identity_library.py
index 70d8f231c..aba565f5c 100644
--- a/pysindy/feature_library/identity_library.py
+++ b/pysindy/feature_library/identity_library.py
@@ -1,10 +1,7 @@
-from sklearn.utils.validation import check_is_fitted
+from .polynomial_library import PolynomialLibrary
 
-from .base import BaseFeatureLibrary
-from .base import x_sequence_or_item
 
-
-class IdentityLibrary(BaseFeatureLibrary):
+class IdentityLibrary(PolynomialLibrary):
     """
     Generate an identity library which maps all input features to
     themselves.
@@ -32,70 +29,5 @@ class IdentityLibrary(BaseFeatureLibrary):
     ['x0', 'x1']
     """
 
-    def get_feature_names(self, input_features=None):
-        """
-        Return feature names for output features
-
-        Parameters
-        ----------
-        input_features : list of string, length n_features, optional
-            String names for input features if available. By default,
-            "x0", "x1", ... "xn_features" is used.
-
-        Returns
-        -------
-        output_feature_names : list of string, length n_output_features
-        """
-        check_is_fitted(self)
-        n_input_features = self.n_features_in_
-        if input_features:
-            if len(input_features) == n_input_features:
-                return input_features
-            else:
-                raise ValueError("input features list is not the right length")
-        return ["x%d" % i for i in range(n_input_features)]
-
-    @x_sequence_or_item
-    def fit(self, x_full, y=None):
-        """
-        Compute number of output features.
-
-        Parameters
-        ----------
-        x : array-like, shape (n_samples, n_features)
-            The data.
-
-        Returns
-        -------
-        self : instance
-        """
-        n_features = x_full[0].shape[x_full[0].ax_coord]
-        self.n_features_in_ = n_features
-        self.n_output_features_ = n_features
-        return self
-
-    @x_sequence_or_item
-    def transform(self, x_full):
-        """Perform identity transformation (return a copy of the input).
-
-        Parameters
-        ----------
-        x : array-like, shape (n_samples, n_features)
-            The data to transform, row by row.
-
-        Returns
-        -------
-        x : np.ndarray, shape (n_samples, n_features)
-            The matrix of features, which is just a copy of the input data.
-        """
-        check_is_fitted(self)
-
-        xp_full = []
-        for x in x_full:
-            n_features = x.shape[x.ax_coord]
-            n_input_features = self.n_features_in_
-            if n_features != n_input_features:
-                raise ValueError("x shape does not match training shape")
-
-            xp_full = xp_full + [x.copy()]
-        return xp_full
+    def __init__(self):
+        super().__init__(degree=1, include_bias=False)