[Ethereum] Create contract in Go-ethereum with Solidity, “Hello world” program

I want to create contract in go-ethereum using Solidity, I started with "Hello world" program.

I create a private network:

$geth --genesis private.json --networkid 1234 --datadir /home/user/Documents/genesisdata  console

In here, I make a new account then I coded follow link https://www.ethereum.org/greeter.

var greeterSource ='contract mortal { address owner; function mortal() { owner = msg.sender; } function kill() { if (msg.sender == owner) selfdestruct(owner); } } contract greeter is mortal { string greeting; function greeter(string _greeting) public { greeting = _greeting; } function greet() returns (string) { return greeting; } function test() returns (string){ return greeting; } }'

And I got: undefined

When I code without var like this:

greeterSource ='contract mortal { address owner; function mortal() { owner = msg.sender; } function kill() { if (msg.sender == owner) selfdestruct(owner); } } contract greeter is mortal { string greeting; function greeter(string _greeting) public { greeting = _greeting; } function greet() returns (string) { return greeting; } function test() returns (string){ return greeting; } }'

I got:

"contract mortal { address owner; function mortal() { owner =
msg.sender; } function kill() { if (msg.sender == owner)
selfdestruct(owner); } } contract greeter is mortal { string greeting;
function greeter(string _greeting) public { greeting = _greeting; }
function greet() returns (string) { return greeting; } function test()
returns (string){ return greeting; } }"

So I continute code without var, I compile:

greeter = greeterContract.new(_greeting,{from:web3.eth.accounts[0], data: greeterCompiled.greeter.code, gas: 210000}, function(e, contract){
if(!e) {

  if(!contract.address) {
    console.log("Contract transaction send: TransactionHash: " + contract.transactionHash + " waiting to be mined...");

  } else {
    console.log("Contract mined! Address: " + contract.address);
    console.log(contract);
  }

}
else{
console.log("Error:>>>>>>>>>>>>>");
console.log(e);
}

})

untill:

greeter.greet();

TypeError: 'greet' is not a function
at :1:1

I don't know, how to solve it.

Please show me the problem that I make in this process.

Thanks.