img: https://fastapi.tiangolo.com/img/sponsors/scalar.svg
  - url: https://www.propelauth.com/?utm_source=fastapi&utm_campaign=1223&utm_medium=mainbadge
    title: Auth, user management and more for your B2B product
    img: https://fastapi.tiangolo.com/img/sponsors/propelauth.png
  - url: https://www.withcoherence.com/?utm_medium=advertising&utm_source=fastapi&utm_campaign=website
    title: Coherence

    checkState(count() > 1);
    return sumOfProductsOfDeltas / (count() - 1);
  }

  /**
   * Returns the <a href="http://mathworld.wolfram.com/CorrelationCoefficient.html">Pearson's or
   * product-moment correlation coefficient</a> of the values. The count must greater than one, and
   * the {@code x} and {@code y} values must both have non-zero population variance (i.e. {@code

typical or common use of that class of product, regardless of the status
of the particular user or of the way in which the particular user
actually uses, or expects or is expected to use, the product.  A product
is a consumer product regardless of whether the product has substantial
commercial, industrial or non-consumer uses, unless such uses represent
the only significant mode of use of the product.

        axesSizeProduct[i] = IntMath.checkedMultiply(axesSizeProduct[i + 1], axes.get(i).size());
      }
    } catch (ArithmeticException e) {
      throw new IllegalArgumentException(
          "Cartesian product too large; must have size at most Integer.MAX_VALUE");
    }
    this.axesSizeProduct = axesSizeProduct;
  }

  private int getAxisIndexForProductIndex(int index, int axis) {

      return BigInteger.valueOf(LongMath.factorial(n));
    } else {
      int k = 20;
      return BigInteger.valueOf(LongMath.factorial(k)).multiply(oldSlowFactorial(k, n));
    }
  }

  /** Returns the product of {@code n1} exclusive through {@code n2} inclusive. */
  @SuppressWarnings("UseCorrectAssertInTests") // TODO(b/345814817): Remove or convert assertion.
  private static BigInteger oldSlowFactorial(int n1, int n2) {

//     compression). This is an optional area; by default, there should be no <SystemRecommendations> section in the
//     system.xml. Vendors can work with Veeam Product Management and the Alliances team on getting approval to integrate
//     specific system recommendations based on current support case statistics and storage performance possibilities.

### Cross-cutting architecture modules

There are some additional cross-cutting architecture modules that aren't themselves platforms:

#### Enterprise integration

Provides cross-cutting integration with Gradle's commercial product.

#### IDE integration

Provides cross-cutting integration with IDEs and other tooling.

#### Build infrastructure

        <img class="sponsor-image" src="/img/sponsors/scalar-banner.svg" />
      </a>
    </div>
    <div class="item">
      <a title="Auth, user management and more for your B2B product" style="display: block; position: relative;" href="https://www.propelauth.com/?utm_source=fastapi&utm_campaign=1223&utm_medium=topbanner" target="_blank">
        <span class="sponsor-badge">sponsor</span>

## Cross-cutting architecture modules

There are some additional cross-cutting architecture modules that aren't platforms:

### Enterprise integration

Provides cross-cutting integration with Gradle's commercial product.

### IDE integration

Provides cross-cutting integration with IDEs and other tooling.

### Build infrastructure

    checkState(count() > 1);
    return sumOfProductsOfDeltas / (count() - 1);
  }

  /**
   * Returns the <a href="http://mathworld.wolfram.com/CorrelationCoefficient.html">Pearson's or
   * product-moment correlation coefficient</a> of the values. The count must greater than one, and
   * the {@code x} and {@code y} values must both have non-zero population variance (i.e. {@code