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fix #13 
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‎docs/src/api_cone_types.md‎

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# [Supported Cone Types](@id api-cone-types)
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Clarabel natively supports optimization problems with conic constraints defined on the following cones:
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Cone Type| Constructor | Definition
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----- | :----- | :-----
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Zero cone | `ZeroConeT(n)` | ``\{ 0 \}^{n}``
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Nonnegative Orthant | `NonnegativeConeT(n)` | ``\{ x \in \mathbb{R}^{n} : x_i \ge 0, \forall i=1,\dots,\mathrm{n} \}``
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Second-Order Cone | `SecondOrderConeT(n)` | ``\{ (t,x) \in \mathbb{R}^{n} : \|\|x\|\|_2 \leq t \}``
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Exponential Cone | `ExponentialConeT()` | ``\{(x, y, z) : y > 0,~~ ye^{x/y} ≤ z \}``
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Power Cone | `PowerConeT(a)` | ``\{(x, y, z) : x^a y^{(1-a)} \geq \|z\|,~ (x,y) \geq 0 \}`` with ``a \in (0,1)``
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Generalized Power Cone | `GenPowerConeT(a,n)` | ``\{(x, y) \in \mathbb{R}^{len(a)} \times \mathbb{R}^{n} : \prod\limits_{a_i \in a} x_i^{a_i} \geq \|\|y\|\|_2,~ x \ge 0 \}`` with ``a_i \in (0,1)`` and ``\sum a_i = 1``
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Positive Semidefinite Cone (triangular part) | `PSDTriangleConeT(n)` | Upper triangular part of the positive semidefinite cone ``\mathbb{S}^{n}_+``. The elements ``x`` of this cone represent the columnwise stacking of the upper triangular part of a positive semidefinite matrix ``X \in \mathbb{S}^{n}_+``, so that ``x \in \mathbb{R}^d`` with ``d = {n(n+1)}/{2}.``
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| Cone Type | Constructor | Definition |
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| -------------------------------------------- | :---------------------- | :---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
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| Zero cone | `ZeroConeT(n)` | ``\{ 0 \}^{n}`` |
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| Nonnegative Orthant | `NonnegativeConeT(n)` | ``\{ x \in \mathbb{R}^{n} : x_i \ge 0, \forall i=1,\dots,\mathrm{n} \}`` |
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| Second-Order Cone | `SecondOrderConeT(n)` | ``\{ (t,x) \in \mathbb{R}^{n} : \|\|x\|\|_2 \leq t \}`` |
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| Exponential Cone | `ExponentialConeT()` | ``\{(x, y, z) : y > 0,~~ ye^{x/y} ≤ z \}`` |
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| Power Cone | `PowerConeT(a)` | ``\{(x, y, z) : x^a y^{(1-a)} \geq \|z\|,~ (x,y) \geq 0 \}`` with ``a \in (0,1)`` |
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| Generalized Power Cone | `GenPowerConeT(a,n)` | ``\{(x, y) \in \mathbb{R}^{len(a)} \times \mathbb{R}^{n} : \prod\limits_{a_i \in a} x_i^{a_i} \geq \|\|y\|\|_2,~ x \ge 0 \}`` with ``a_i \in (0,1)`` and ``\sum a_i = 1`` |
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| Positive Semidefinite Cone (triangular part) | `PSDTriangleConeT(n)` | Upper triangular part of the scaled positive semidefinite cone ``\mathbb{S}^{n}_+``. The elements ``x`` of this cone represent the columnwise stacking of the scaled upper triangular part of a positive semidefinite matrix ``X \in \mathbb{S}^{n}_+``, so that ``x \in \mathbb{R}^d`` with ``d = {n(n+1)}/{2}.``   When extracting the upper triangular part of the matrix, off-diagonal terms are scaled by ``\sqrt{2}`` so that inner products are preserved. |

‎docs/src/examples/example_sdp.md‎

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where $\mathcal{K}_{\text{tri}}^n$ is the cone of vectors representing the triangular part of matrices in $\mathbb{S}_+^n$.
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For the equality constraint can we must be careful to rewrite the inner product on $X$ in a form that is an equivalent linear function of $x$. We therefore write
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For the equality constraint we must be careful to rewrite the inner product on $X$ in a form that is an equivalent linear function of $x$. We therefore write
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```math
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\begin{aligned}
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\langle A,X\rangle &= \textrm{vec}(A)^T\textrm{vec}(X) \\

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