# from the theory of proveit.physics.quantum.algebra¶

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit.linear_algebra import ScalarMult, VecAdd, VecNeg
from proveit.logic import Equals
from proveit.numbers import frac, one, sqrt, two
from proveit.physics.quantum import ket0, ket1, ket_minus

In [2]:
# build up the expression from sub-expressions
expr = Equals(ket_minus, ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, VecNeg(ket1))))

Out[2]:
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\lvert - \rangle = \left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(-\lvert 1 \rangle\right)\right)\right)

In [5]:
stored_expr.style_options()

Out[5]:
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()

Out[6]:
core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 27
operand: 8
4Operationoperator: 6
operands: 7
5ExprTuple8
6Literal
7ExprTuple9, 10
8Literal
9Operationoperator: 25
operands: 11
10Operationoperator: 12
operands: 13
11ExprTuple30, 14
12Literal
13ExprTuple15, 16
14Operationoperator: 17
operands: 18
15Operationoperator: 27
operand: 23
16Operationoperator: 20
operand: 24
17Literal
18ExprTuple29, 22
19ExprTuple23
20Literal
21ExprTuple24
22Operationoperator: 25
operands: 26
23Literal
24Operationoperator: 27
operand: 30
25Literal
26ExprTuple30, 29
27Literal
28ExprTuple30
29Literal
30Literal